Midas Ngen Manual

midas nGen

Design Manual

DISCLAIMER Developers and distributors assume no responsibility for th e use of MIDAS Family Program (midas Civil, midas FEA, midas FX+, midas Gen, midas Drawing, midas SDS, midas GTS, SoilWorks, SoilWorks, midas midas NFX, NFX, midas Drawing Drawing,, midas nGen ; here in after after referred referred to as “MIDAS “MIDAS package”) or for for the accuracy or validity of any any results obtained from the MIDAS package. package. Developers and distributors shall not be liable for loss of profit, loss l oss of business, or financial loss which may be caused directly or indirectly by the MIDAS package, when used for any purpose or use, due to any defect or deficiency therein. Accordingly Accordingly,, the th e user is encouraged encouraged to fully understand the bases of the program and become become familiar with the users manuals. The user shall also independently verify the results produced by th e program.

INDEX Chapter1. Introduction Outline

4

Design Capabilities

5

Chapter2. Steel Design Outline

53

Design Factor Factor – AISC360 AISC360-10 -10

70

Member Examination Procedure

78

Design Parameters-EN1993-1-1:2005

89

Member Examination ProcedureEN1993-1-1:20015 Cross-Section Computations

96 112

Chapter3. RC Design Outline

119

Rebar/Arrangement

123

Common Design Considerations

132

Design Considerations-ACI318-11

135

Member Examination Procedure (Beams)-ACI318-11

139

Member Examination Procedure (Columns/Braces) ACI318-11

152

Design Parameters EN1992-1-1:2004

167

Member Examination Procedure (Beams) – EN1992-1-1:2004

169

Member Examination Procedure (Columns/Braces) -EN1992-1-1:2004

187

Rebar/Arrangement

201

Chapter 1. Introduction

DESIGN DESI GN REF REFEREN ERENCE CE

S e ct c t io n 1

Outline The design capabilities capabilities of midas nGen 7 Foundation include include steel design, reinforced concrete design, and basic member design/strength checks. For steel members, the program offers the ability to conduct cross section calculations, which form the basis of the member design strength. For reinforced concrete members, the program offers the ability to conduct cross section and reinforcement calculations. To conduct member design and strength checks, the analysis of the structure of design interest must be linearized. Design parameters for the computations may include force/moment results output from static or dynamic analysis, as well as the cross section characteristics, characteristics, material properties, and other m ember information that is input at the creation of the model. When cre ating the analysis analysis mo del, design design criteria criteria for each mem ber may be specified using the design variable input window. If the user does not specify values for certain design variables, the program uses the default values. After using the “Run Design” option, the member design results may be verified through various options. The program offers the ability ability to run graphic post-process ing on the results, and the outputs can be seen in tabular or list list format as w ell.

Sect Se ctio ion n 1. Ou Outl tlin ine e|1


DESIGN REFERENCE

S e ctio n 2

2.1 Design Groups

D esign C apa bilities Design groups categorize members with the purpose of obtaining comm on computation results. The following conditions are considered to auto-generate design groups, and the groups may be manually mo dified by the user. ► Mem bers of a group are of the same type (beam, column, brace, wall, slab). ► Mem bers of a group have the s ame characteristics (section, thickness, material). ► If the reinforcement has been calculated, the reinforced concrete members of a group have

the same reinforcement.

Figure 1.2.1 Dialog window for Auto-Generating Design Groups

2 | Section 2. Design Capabilities


DESIGN REFERENCE

When auto-generating design groups, the naming conventions for the different member types are as follows. Beams ► LOD1 (Level of Detail 1) : Exterior and interior beams are differentiated from one another

and are grouped as such. Beam s on different levels are categorized into different groups. ► LOD2 (Level Of Detail 2) : Beams that are not continuous based on the LOD1 results are categorized in separate groups and thus LOD 2 allows the user to obtain a more subdivided level of grouping.

F ig u re 1 .2 . 2 B e a m N a m i ng Convention

Only grouped into interior and exterior beams

Discontinuous beams are grouped separately

Sub Beams ► LOD1 (Level of Detail 1) : Sub beams of the same level, measurements, and reinforcement

are categorized into the sam e group.

Section 2. Design Capabilities | 3


DESIGN REFERENCE

► LOD2 (Level Of Detail 2) : Discontinuous beams based on the LOD1 results are categorized

in separate groups and thus LOD2 allows the user to obtain a more subdivided level of grouping.

Columns

Groups categorize columns into corner columns, exterior columns, and interior columns.

F ig u re 1 .2 . 3 C o lu m n Naming Convention

E levation V iew

P lan View

Sub Columns

Continuous sub columns are grouped together, and all other exceptions are grouped separately. Braces

Braces are separated into groups based on the analysis characteristics. Braces with the same analysis type, materials, and cross section are g rouped together. ► Beam-Brace : Braces analyzed as beam elements ► Truss-Brace : Braces analyzed as truss elements ► Tens. Only : Braces analyzed as tension-only elements ► Comp. Only : Braces analyzed as compression-only elements Plates

Plates are separated into one group per memb er.



DESIGN REFERENCE

2.2 Design Load Combinations

Load Combination Types

Load com binations for design are decided based on load types and num bers of com binatio ns. Thus, it is important to confirm whether the defined load combination is appropriate for the design purpose, before procee ding with structural memb er design. Load com binations for each country and design purpose are shown below.

Table 1.2.1 Load Combination Types depending on Country and Design Purpose

S tr en gth Serviceability

L oa d co m bin at io n fo r stre ng th v er ific atio n Load combination for serviceability verification

Special

Load combination for earthquake scenarios

Vertical

Load combination for strength verification in vertical earthquake ground motions - Used for design of members with pre-stressing

F atig ue

L oa d c om bin at io n fo r fatig ue v erif ic atio n

S tr en gth

L oa d co m bin at io n fo r stre ng th v er ific atio n

Serviceability

Special

Vertical

Fundamental A c ci de nt al S eis mic Characteristic Frequent QuasiPermanent

strength

verification

special

Load combination for serviceability verification Load combination for strength verification in special earthquake scenarios - Used for design of members that may cause a sudden break in earthquake load through instability or collapse. Load combination for strength verification in vertical earthquake ground motions - Used for design of members with pre-stressing. Load combination for strength verification (Persistent & Transient) L o ad c o m bin at io n f or s tr en g th v er if ic at io n (A c c id en ta l) L oa d co m bin at io n fo r stre ng th v er ific atio n (S eis m ic ) Load combination for serviceability verification - Used for stress verification of reinforced concrete mem bers Load combination for serviceability verification - Used for cracking in reinforced concrete members. Load combination for serviceability verification -Used for cracking/stress verification in reinforced concrete members.

F atig ue

L oa d c om bin at io n fo r fatig ue v erif ic atio n

S tr en gth

L oa d co m bin at io n fo r stre ng th v er ific atio n

Serviceability

in

Load combination for serviceability verification Section 2. Design Capabilities | 5

DESIGN REFERENCE




DESIGN REFERENCE

Definition and Application of Load C ombinations

In this program, pre-defined load combination templates may be used. Alternatively, the user may manually specify load combinations. The pre-defined, design-based load combination templates are already stored for easy use within the program. The user may modify the template files to apply the appropriate load combination. The file directory for the temp late is as follows:

Program A pplication Folder>Design>LoadCom bination>M aterial Folder(RC, … )>Design Standard Folder(ACI 318-11 , …)

Load com bination template file name e xtensions are text files, and the main content format is shown below.

*VERSION 1.0.0 *CODE A ISC360-10(LRF D ) *DTYP STEEL

// in A SCE /SE I 7-10.

D, L, LR, S, R, FP, WX:AL, WY :AL, W:AL, EQX:AL, EQY:AL, EQV:AL, EQ:AL, RSX:AL, RSY:AL, RSV:AL, RS:AL // A : Alternation (+/-), L : Loop, each load set STRN , SERV, SPECSEIS, VERTSE IS, FATG // Strength(General), Serviceability(Genera), Strength(Special Seismic), Strength(Vertical Seismic) LCB1, ADD 1.4*D, 1.4*FP


DESIGN REFERENCE

8 | Se Secti ction on 2. De Desig sign n Cap Capabi abili liti tie es



DESIGN REFERENCE

► LTYP : This defines the load types that are incorporated into into the load combinations.

This may be verified from from H ome > Define > Set > Load Set > Static Static Load Set. The load types may be selected from the Load T ype list that is is pre-defined w ithin ithin the program . In In particular, the specified specified keyw ords mu st be used in order to apply the desired load types, such as “D ” for dead loads and “L” for live loads. Figure 1.2. Figure 1.2.44 Stat Static ic Load Set Dialog Window

Table 1.2. 1.2.22 Load Types and Keywords

D ead Load

D

L iv e L o a d

L

R o o f L iv e L o a d

LR

W in d L o a d o n S t r u c t u r e

W

May be defined as WX, WY (Combination of both directions)

E arth quake

EQ

May be defined as EQX, EQ Y (Combination of both directions)

V e r it ic a l E a r t h q u a k e

EQV

Snow Load R a in L o a d

S R

Ic e L o a d

IC

E arth P ress u re

EP

H o r iz o n a l E a rt h P r e s s u r e

EH

V e r t ic a l E a r t h P r e s s u r e

EV

G ro und W ate r P res s ure

WP

F lu id P r e s s u r e B uoyancy

FP B

T em pe rature

T

L iv e L o a d Im p a c t

IL

Collision Load

CO

U s e r D e f in e d L o a d

U SER

Sect Se ction ion 2. De Desig sign n Cap Capab abili ilitie ties s|9

DESIGN REFERENCE

10 | Sec Secti tion on 2. De Desig sign n Cap Capab abil ilit itie ies s



DESIGN REFERENCE

When defining the load type, two additional options are available to further specify load characteristics. characteristics. Either or both options m ay be used. Table 1.2.3 Additional options for load types

(Load Type)

(Load Type):L

This option option refers to alternative( alternative(+/-) +/-) loads. Load Load combinations for for both directions of the applicable load types are created. (Ex.) When adding adding the option option W:A to the load load type and combination combination set LCB1, ADD, 1.0*D, 1.0*W, 1.0*W, the followin followingg load combinati combinations ons are created: LCB1_1 : 1.0*D + 1.0*W LCB1_2 : 1.0 1.0*D *D - 1.0*W 1.0*W This option means to “loop each load set”. Load combinations for each applicable load type are created. (Ex.) When adding adding the option option L:L to the the load load set L1, L2, L3 and load load definit definition ion LCB1, ADD, 1.0*D, 1.0*L 1.0*L,, the followi following ng load combinati combinations ons are created: LCB1_1 : 1.0*D + 1.0*L1 LCB1_2 : 1.0*D + 1.0*L2 LCB1_3 : 1.0*D + 1.0*L3

► CTYP : This refers to the design load combination. Depending on the design criteria, the

load combination type changes, and the type is defined within the tabs in the “Define Load Combination” Combination” dialog dialog window. window. F ig ig u re re 1 .2 .2 . 5 D e f in in e L o a d Combination Combinat ion Dial Dialog og Windows

Secti Se ction on 2. Des Design ign Capa Capabil bilitie ities s | 11


DESIGN REFERENCE

T a bl e 1 .2 .4 L o ad Combination Types and Keywords


ST R N SE R V

Strength Serviceability

SP E CSE IS

Strength > Special Seism ic ( A SCE , KB C)

VE R TSE IS

Strength > Vertical Seism ic ( A SCE , K BC)

FU ND A C CD

Strength > Fundam ental Strength > A ccidental

SE IS

Strength > Seism ic

CHA R

Serviceability > Characteristic

FRE Q

Serviceability > Frequent

QUAS

Serviceability > Q uasi-perm anent

FA T G SH R T

Fatigue Short Term

LO N G

Load Term

STR N 1

Strength1

STR N 2 STR N 3

Strength2 Strength3

STR N 4

Strength4

STR N 5 E XT R 1

Strength5 E xtrem e E vent1

E XT R 2

E xtrem e E vent2

SE R V1

Serviceability1

SE R V2 SE R V3

Serviceability2 Serviceability 3

SE R V4 FA T G1

Serviceability 4 Fatigue1

FA T G2

Fatigue2


DESIGN REFERENCE

► COMB-■■■■ : This defines the load combinations that apply to different load types. The

user may input the name of the load combination, the sum type, and the load combination number. The sum types for load combinations are shown below. T a b le 1 .2 .5 S u m t y pe s o f m i d as n G e n l oa d combinations

A DD

Linear Sum

1.2 D +1.6L

ABS

A bsolute Sum

1.2 D + 1.6 L

SR SS

Square R oot of Sum of Squares

E N VE LO P

E nvelope

(1.2 D) 2 + (1.6L)

2

max[1.2 D,1,6 L ] min[1.2 D,1.6 L]

Nonlinear Load Combinations

When conducting nonlinear analysis, the user must select a load combination for iterative analysis. In nonlinear analysis, only sum type load com binations may be selected. In iterative analysis, nonlinear elements such as tens ion-only and com pression-only elements experience varying loads and stiffnesses depending on the strain and stress caused by different external loads. Thus, it is not feasible to obtain accurate results through the linear sum of load com binations. Thus, as shown in Figure 1.2.6, in a structure with tension-only elements, the linear sum of analysis using two different loads is not equal to the result of using both loads at once .

F ig ur e 1 .2 .6 C o m pa ris on of results of a structure with tension-only elements

Axial force (A) in tension-only members due to Load 1:

A≠0



DESIGN REFERENCE

Axial force (B) in tension-only members due to Load 2: L in ea r s um o f th e ax ia l fo rc es f or Lo ad 1 an d Lo ad 2 : Axial force using a nonlinear load combination (simultaneous combination of load 1 and load 2) :


B=0 A+B≠0 0 (Zero axial force due to simultaneous loading)


DESIGN REFERENCE

In order to obtain the internal force of such a nonlinear element, unit load criteria must be applied to each load combination.

In the program, the load combination information may be

interpreted as unit loads when load combinations are defined (the NL Check option shown below in Figure 1.2.7). F ig u re 1 .2 . 7 L o a d Combination Editing Dialog Window

Set loop-option The loop-option is used to create specific load combinations that are created from load sets including loads of the same load type that should not be repeated in the same l oad combination. If the Auto Generate Load Combination function is used, then load combinations are created using the sums of loads belonging to the sam e load types. When creating load combinations using the results of m oving crane analysis, it is important to be aware o f certain load results that should not be repeated w ithin the sam e load comb ination. In such a case, the loop-option m ay be set to define the required load combinations. Consider the example of reaction forces calculated through moving crane analysis. Without using the loop condition and instead using the Auto Generate Load Combination function, all live loads are all included s imultaneously within the same load combination. Section 2. Design Capabilities | 15


DESIGN REFERENCE

F ig u re 1 .2 . 8 L o a d combinations that are defined as a result of using the Auto Generate Load Combination function

Repeating vertical and horizontal loads and axial loads in the same load combination may lead to an over-design of the structure. Each load combination should include one vertical, one horizontal, and one axial load to create an appropriate design. In this cas e, three Loop G roups are defined and the different loads are categorized into the appropriate Loop Groups. Define Load Combinations > Generate Load Comb inations by Temp late > Set loop - option F ig u re 1 .2 . 9 L o a d combinations that are defined as a result of using the Loop Option



DESIGN REFERENCE

Using the Loop Condition function, six load combinations for the load combination equation LCB2 (1.2*D+1.6*L) have been created. The automated load combinations using the loop option are shown below. T a bl e 1 .2 .6 L o ad combinations automatically created with loop conditions

Conditions

Dead Loads: DL, CL Live Loads: CL1(V), CL2(V), CL3(H ), CL4(H ), CL5(L), CL6(L) Load Com bination Equation: LCB2 = 1.2*D + 1.6*L

Load Combinations without using Loop Conditions

1.2D+1.6*(LL+CL1(V)+CL2(V)+CL3(H)+CL4(H)+CL5(L)+CL6(L))

Load Combinations using Loop Conditions

1.2*D+1.6*(LL+CL1(V)+CL3(H)+CL5(L)) 1.2*D+1.6*(LL+CL2(V)+CL3(H)+CL5(L)) 1.2*D+1.6*(LL+CL1(V)+CL4(H)+CL5(L)) 1.2*D+1.6*(LL+CL2(V)+CL4(H)+CL5(L)) 1.2*D+1.6*(LL+CL1(V)+CL4(H)+CL6(L)) 1.2*D+1.6*(LL+CL2(V)+CL4(H)+CL6(L))



DESIGN REFERENCE

Member Load Combinations

Member-specific load combinations may be selected from the load combinations that have already been created. The user may manually specify load combinations to be applied to a specific member and this load combination may differ from those being applied to other structural members, usually for a s pecific design purpos e. F ig u re 1 .2 . 10 M e m b e r L o ad Combination Dialog Window

The load combinations with Check-On status are used in strength verificati on or reinforcement definition. The load combinations with Check-Off status are not used in strength verification o r reinforcement definition.



DESIGN REFERENCE

2.3 Member Parameters

Effective Length Factors

If the axial compression force of a compressive member is small, the column length may be slightly reduced. Ho wever, if the compressive force increases and reaches a certain threshold, then the element may sudd enly buckle. The buckling behavior of a column element depends o n the cross-section properties, material properties, column length, and boundary conditions. Columns should be designed to avoid buckling behavior. The effective length factor of a column element should be calculated using an alignment chart or by using a representative effective length factor based on the boundary conditions at the two ends. Of course, using the alignment chart to determine the effective length factor for all columns of a model is quite burdensome. The program allows for internal, automated calculations of the effective length factors for column elements. The effective length factor is decided base d on whe ther or not side sw ay is inhibited — this decides whether the structure is compo sed of a braced frame or unbraced frame. Braced frames do not permit lateral movement as they have a structural member that resists such movement (e.g. shear walls, braces). Thus, braced frames prevent lateral movement through bracing elements other than the frame. Oftentimes in actual structures, however, braces may exist in only one direction or installed in only one po rtion of the structure. Thus, it is not often easy to differentiate braced fram es from unbraced frames. In the automated procedure for calculating the effective length factor, many as sumptions are required. Thus, it is important to ens ure that the autom atically calculated values are realistic. The automated calculations for the effective length factor of all elements within a model are set up in the Design Parameters dialog window. Home>Design Settings>General>Design Code

F ig u re 1 .2 . 11 D e s ig n Parameters Dialog Window



DESIGN REFERENCE

For each m ember, the user m ay allow the program to determ ine the effective length factor or may specify a value for the program to use. This may be done in the Member Design Parameters dialog window. An al ys is & D es ign > Member Parameters > Member Parameters Figure 1.2.12 Member Design Parameters Dialog Window

The automatically calculated length factor may be verified in the Design Report and the Design Results (Graphics window).



DESIGN REFERENCE

Result>Design Result>Design Report Figure 1.2.13 Effective Length Factor w ithin the Design Report

Result>Design Result>Effective Length Factor (K factor)>Ky, Kz Figure 1.2.14 Effective Length Factor w ithin the Design Results (Graphic Interface)

► Algorithm for Determining the Effective Length Factor

K represents the effective length factor, and given the relationship X=π/K, the equations of equilibrium for braced and unbraced frames are as follows.

Braced F ra me

F ( X )

:

=

G AGB

4

X

2

X é G + GB ù é 1+ê A ú ê 2 ë û ë tan X

ù 2 éX ú + X tan ê 2 û ë

ù ú -1 = 0 û

(1.2.1)



DESIGN REFERENCE

Unbraced F ra me :

F ( X )

=

G AGB X

2

- 36

6(G A + GB )

-

X

tan X

=0

(1.2.2)

The following assumptions lead to the above equations of equilibrium. 1. All of the motion rem ains within the elastic region. 2. The members are prismatic. 3. All columns simultaneously experience buckling loads. 4. Structures are symm etrically braced. 5. The restraining moment due to a girder at a node is distributed to the columns based on the stiffness of each column. 6. Girders are elastically restrained at each end with the columns, and when buckling occurs, the rotational displacement of each end of the girder has the equal m agnitude and opposite direction. 7. Girders do not support axial loads.



DESIGN REFERENCE

The solution to this nonlinear equation is found through the Newton-Raphson method. The iterative relationship is sho wn below.

X 2

=

X 1

-

F ( X ) F

(1.2.3)

'( X )

The solution to the equation involves tanX and tan(X/2) within F ( X ) an d

F ' ( X ) ,

which may

become zero or infinite. This program takes this into consideration and ensures that a stable solution is always reached.

Figure 1.2.15 Th e e ffective length (KL) of a column with two restrained end s

P

P P

P

KL=0.7L KL
KL=0.5L

KL=L

P

P

P

P

(c ) One End Restrained,



DESIGN REFERENCE

P

Figure 1.2.16 Effective length (KL) of a column with one free end

P P

L L

L

KL>2L KL=L

KL=2L

Partial Restrain

P


P

P


DESIGN REFERENCE

Figure 1.2.17 Effective length of braced and unbraced frames

P

P

L

P

0.7L
KL 2

KL>2L

L

(a) B raced F ram e, H inged B ase

P

(b) U nbraced F ram e, H inged B ase

P P

L

P

0.5L
P

L

L
(c) Braced Frame, Fixed Base

(d)

Unbraced Frame, Fixed



DESIGN REFERENCE

T a b le 1 .2 .7 E f fe c ti v e length factor (K) of columns with different end conditions

a

b

c

d

e

f

0.5

0.7

1.0

1.0

2.0

2.0

0.65

0.8

1.0

1.2

2.1

2.0

Buckled shape of the column shown by dashed line

Theoretical value Recommended design values when ideal conditions are approximated

Rotation fixed, Translation fixed Rotation free, Trans lation fixed End conditions code Rotation fixed, Translation free Rotation free, Translation free



DESIGN REFERENCE

Unbraced Length

The unbraced length of a member is determined with respect to both the y- and z-axis directions (in the element coordinate sys tem). When a member is subject to axial force or bending moment, the length that experiences bending strain along the element major axis (y-axis) and minor axis (z-axis) in the element coordinate system is called the unbraced length (see F igure 1.2.18). The unbraced length of a mem ber is used along with the effective length factor. The unbraced length also is incorporated in calculations for the slenderness ratio, which is required in computing the design axial compressive strength or allowable compress ive force. F ig u re 1 .2 . 18 U n b r ac e d length of a member

Minor Axis (z-Axis)

Major Axis (y-Axis)

) s a x i r o j a t m u o b t h a g n d l e e c a n b r U ( L y ) s a x i r o m i n t u b o h a t g n d l e e c a n b r U ( L z

The automatic calculations for the unbraced lengths of all members within a model are set up in the Design Parameters section of each Design Code.

Home>Design Settings>General>Design Code

F ig u re 1 .2 . 19 D e s ig n Parameters Dialog Window



DESIGN REFERENCE

The unbraced length may be left to be determined by the program or the user may specify a value for the program to use. This can be defined within the Member Design Parameters dialog window for each member. Analysis & Design>Analysis & Design>Member Parameters>Member Parameters 그 림 1 .2 .2 0 M e m b er D e sig n Parameters Dialog Window



DESIGN REFERENCE

The automatically computed lengths may be seen in the Design Report and the Design Results (graphic interface). Result>Design Result>Design Report Figure 1.2.21 Unbraced Length shown in the Design Report

Result>Design Result>Unbraced Length>Ly, Lz, Lb Figure 1.2.22 Unbraced Length shown in the Design Results (graphic interface)



DESIGN REFERENCE

The following exam ple illustrates the calculation of a n unbraced length for a typical case.

Figure 1.2.23 Unbraced length for major and minor axis of a member, CASE 1 Girder

C3

C4

C1

C2

L/2

L/2` L

Figure 1.2.24 Unbraced length for major and minor axis of a member, CASE 2

3 L 1 L

C4

C3

C6

2 L

C1

C2

C3

A : Ly = L2, L z = L1 Unbraced length of a c olumn ○ B : Ly = L3, L z = L1 Unbraced length of a c olumn ○ C : Ly = Lz = L1 Unbraced length of a c olumn ○

< CASE 2 >



DESIGN REFERENCE

Figure 1.2.25 The relationship between the analytical model elem ents and the unbraced lengths 4 ○

3 ○

3 C L

2 C L

B ○ 1 ○

1 C L

A ○

C4

LB1 LB3

Element A Column ○ B Colum n ○ C Colum n ○ Colum n E Colum n ○ F Colum n ○ Beam Beam ○ 2 4 3○ B eam ○ B eam

Node

2 ○ E ○

C ○

C2 LB2

C1

T a bl e 1 .2 .8 T h e relationship between the analytical model elements and the unbraced lengths

F ○

D ○

Node

Unbraced length (Ly) about the element major axis (y-axis) LC 1 LC2 LC1 LC2 LC3 LC3 LB 3 LB 3 LB 4 LB 4

C3 LB4

Unbraced length (Lz) about the element minor axis (z-axis) LC1 LC2 LC3 LC3 LC3 LC3 LB 3 LB 3 LB 4 0

Comments R estrained by slab



DESIGN REFERENCE

Laterally Unbraced Length

If there is a vertical load exerted in the direction parallel to the web of a beam or girder, a vertical deflection occurs on the in-plane side of bending where the moment occurs. As the load increases and eventually passes a certain threshold, the compressive flange of the beam or girder experiences a ho rizontal displacement o utside of the bending plane. As a result, the element may experience rotation and torsion. This phenomenon is called lateral torsional buckling. When this phenomenon occurs, the member can no longer resist the force being exerted on it and may experience sudden failure. Thus, it is important to design beams and girders to prevent lateral torsional buckling. In typical steel mem ber d esign criteria, the lateral torsional buckling failure mode is considered and it is required that the designer calculate the allowab le bending stress or design bending strength. The laterally unbraced length is required to calculate the allowable bending stress (design bending stress), which incorporates lateral torsional buckling considerations. This is the distance along the length of the mem ber in which, under lateral loads, the lateral displacement of the compressive flange is restricted.

Figure 1.2.26 Lateral Torsional Buckling


DESIGN REFERENCE


Figure 1.2.27 Example of Laterally Braced System s

The input for the lateral torsional buckling length and the result of the automated calculation may be verified in the sam e procedure as the unbrace d length.


DESIGN REFERENCE




DESIGN REFERENCE

Live Load Reduction Factor

The live load that is applied to structures are not truly being exerted across the entire floor area. Thus, to achieve reasonable and economical designs, live load reduction factors, shown in Equation 1.2.4, should be used. F = F D + (LLRF)F L + F S

(1.2.4)

Here, : Axial force, moment o r shear force incorporating the live load reduction factor : Axial force, moment, or shear force due to dead loads or other vertical loads

F FD FL

: A xia l f or ce , m o m en t, o r s he ar fo rc e du e t o liv e lo ad s

FS

: Axial force, moment, or shear force due to lateral loads (wind loads, earthquake loads)

L LR F

: L iv e lo ad re du ct io n f ac to r

FD, FL, and F S are factored loads (axial force, moment, or shear force). The live load reduction factor may be calculated as a function of either the tributary area or the number of stories. The calculation procedures for different design codes are show n below. ► ASCE7-05 (Calculated based on the Effective Tributary Area) L =   (0.25 +  . )   T a b le 1 .2 .9 L iv e L o ad Element Factor, K LL

E lem ent

(1.2.5)

K LL *

Interior co lumns Exterior columns without cantilever slabs

4 4

E dge colum ns w ith cantilever slabs

3

Cornor coum ns w ith cantilever slabs Edge bea ms w ithout cantilever slabs Interior beam s

2 2 2

All other mem bers not identified Including: Edge beam s with cantilever slabs Cantilever beams One-way slabs

1



DESIGN REFERENCE

Tow-w ay slabs Mem ber without provisions for continuous Shear transfer normal to their span * In lieu of the preceding values, KLL is permitted to be calculated.



DESIGN REFERENCE

► BS E N 1991-1-1;2002 (Calculated based on the Tributary Area)

  =    +  ≤ 1.0

(1.2.6)

With the restriction for categories C and D :   ≥ 0.6 Here,   is the gactor according to EN 1990 A nnex A1 T able A1.1 A0 = 10m2 A is the loaded area ► BS E N 1991-1-1;2002 (C alculated based on the num ber of stories)    = () 

(1.2.7)

Here, n : is the nunber of storeys (>2) above the loaded structural elements from the same catego ry.

ψ  : is in accordance with EN 1990, Annex A1, Table A1.1 In this program, the live load reduction factor is user-specified, and may be input for each member in the Member Design Parameters dialog window. Analysis & Design>Analysis & Design>Member Parameters>Member Parameters Figure 1.2.28 Member Design Parameters Dialog Window

1



DESIGN REFERENCE

2.4 Check P oints

Depending on the check points within a member, the cross-section stiffness and analysis results may change. Thus, the check point locations greatly affect the design results. To obtain more a ccurate results, check point capabilities have b een installed within this program . In midas Gen, five check points were used for 1-dimensional mem bers. In this program, the user may specify check points for the entire structure or for select structural members. Furthermore, as shown in Figure 1.2.29, mem ber performance may be verified to the left or right of the check point locations. This will allow the user to check for any inconsistencies or unrealistic results that may occur due to conce ntrated loads or mem ber connections.

Figure 1.2.29 Check points of midas nGen

D e f a u lt C h e c k P o i nt s

As shown below, check points may be specified based on the member characteristics. ► Steel Beam/Column/Brace: The number of check points may be specified for each type of mem ber, and element performanc e is verified at the ends of each of the membe r subdivisions. If the number o f check points is five, then the m ember is divided into four sections. Figure 1.2.30 Check point settings dialog window for steel beam/column/braces

► RC Bow/Column : The locations of the check points for RC members are related to the

reinforcement. The locations may be specified with reinforcement considerations. The check


DESIGN REFERENCE


point locations and number of ch eck points may be specified individually with respect to each endpoint and midpoint. Figure 1.2.31 RC Beam/Column Check Points

Figure 1.2.32 Check Point settings dialog window for R C B e am / C o lu m n



DESIGN REFERENCE

► RC B races : Most braces resist axial forces, and the number of check points are defined

regardless of the endpoints and m idpoints. Figure 1.2.33 Check point setting window for RC braces

Advanced Check Po ints

To achieve a more accurate design, locations that may experience a sudden change in force require more thorough inspection and the user may specify additional criteria. The following figures show scenarios in which sudden changes in force may occur. Figure 1.2.34 Advanced Check Points Dialog Window



DESIGN REFERENCE

► Location of concentrated loads

Figure 1.2.35 Location of concentrated loads

► Point of connection with other mem bers

Figure 1.2.36 Point of connection with other members

► Location at which boundary con ditions are applied Figure 1.2.37 Boundary conditions



DESIGN REFERENCE

Member Check Positions

Independent of the check point definitions in Design Setting, check point locations may be defined in selected members. The following figure shows how the design length and number of check points m ay be specified. Figure 1.2.38 Member Check Positions set-up dialog window

2.5 Target Ratio and Design Checking/Decision

T a r g et R a t io

In this program, target ratios are defined for each member type, and the user may also incorporate marginal values when designing the cross section or checking the design strength. Typically, design results are dee med to be ad equate if the inequality shown in E quation 1.2.8 is satisfied. If the target ratio is incorporated into the design, then the inequality shown in Equation 1.2.9 is used instead. Dem and ≤ Capacity D em and ≤ Target R atio X Capacity Here, Demand : Demand strength / stress / deflection Capacity : Strength / force / deflection that the section is capable of handling


(1.2.8) (1.2.9)


DESIGN REFERENCE

Target ratio is used as a criterion for deciding whether the resulting design for steel or RC mem ber sections is satisfactory. For designing reinforcement in RC mem bers, the target ratio also serves to help decide w hether the reinforcement design is satisfactory. The target ratio may be selected differently depending on the member material properties, shape, or other important values. Thus, it is up to the user to decide on the design criteria and marginal values. The target ratio for either the entire structure or for select members in the Design Settings dialog window. Hom e>Design Settings>Check/Decision Figure 1.2.39 Target Ratio set up dialog window

The target ratios for various values may be input in the Member Design Parameters dialog window. Figure 1.2.40 Ta rget Ratio set up in the Memb er Design Parameters dialog window


DESIGN REFERENCE




DESIGN REFERENCE

Design Results and Decisions

The program allows the user to check the design results and provides the design checking process in a more detailed manner, as show n in Figure 1.2.4. Figure 1.2.41 Design Results and Checking

► Need C heck : This is the case in which the design result is smaller than the minimum target

ratio. This often represents overdesign situations, and the user may attempt a more eco nomic design by m odifying the materials, cross sections, and design factors. ► OK : This is the case in which the minimum target ratio < design result ≤ m aximum target ratio. ► Critical : This is the case in which the maximum target ratio < design result ≤ (1.0). The actual behavior should meet performance criteria, but represents a situation in which some members must be checked as the overall design exceeds the maximum target ratio set by the user. ► NG : Design result > (1.0). ► Failure : This only applies to RC mem bers and is available so that users may detect the possibility of brittle failure. In such a case, the member does not perform adequately with only augmenting the steel reinforcement, so it is necessary that the user increase the cross section size or m aterial strength.



DESIGN REFERENCE

As sho wn in Figure 1.2.42, through Design Re sult > Total Result > Status, the membe r design result may be displayed in a visual manner. The design total result ratio is also provided in the interface, so the user m ay m ake a m ore intuitive decision about the total structural result. Figure 1.2.42 Structure design result appearance in the software

Additionally, some design results may be filtered in the table of results, or a specific member’s performance may be verified within the software. Thus, these options allow for quick access to detailed design results. Figure 1.2.43 Structure design result filtering option



DESIGN REFERENCE

2.6 Design Cases

In this program, different analysis cases may be set up with a single model. Each analysis case may be defined to conduct analysis with different target members, loads, and boundary conditions. Thus, even with a single model, a variety of analysis results may be created. Moreo ver, if the design case is defined with the options included in these analysis cases , then various design results may also be created.

Figure 1.2.44 Design Cases set up dialog window

One analysis case is defined within a design case.

The design is conducted using the target members, loads, and boundary conditions defined within the analysis case. After modeling the entire structure and analyzing it, specific members or load conditions may be selected before continuing with design. Using this, various analysis or design cases can be created and separated/merged/connected designs can be conducted and critical members (for each load or type of structural member) can be identified easily. Various design cases are defined.



DESIGN REFERENCE

Various design cases are defined and then ana lysis is conducted. Results for each design case can be seen, and the least optimal case is called the Envelope Design Case. The Envelope Design C ase result is provided to the user to quickly check the structure’s overall appearance. Additionally, when defining design cases, the “Com bined Design Case” ca pability may be used to create com binations of various loading or boundary co nditions. Thus, this capability can b e used in parametric design and the strength results can be quickly combined to apply the results in structural design. Figure 1.2.45 Dialog Window for combining design cases


DESIGN REFERENCE



Chapter 2. Steel Design

DESIGN REFERENCE

S e c t io n 1

Outline Steel members that are included in the analysis model are checked for adequate strength based on a user-specified d esign strength or on the entire steel structure.

The program offers the following design codes.

Table 2.1.1 Design codes categorized per country

AISC360-10(LRFD) AISC360-10(ASD) AISC360-10M(LRFD) AISC360-10M(ASD) AISC360-05(LRFD) AISC360-05(ASD) AISC360-05M(LRFD)

Load and Re sistance Factor Design (US units) Allowable Strength Design (US u nits) Load and Resistance Factor Design (SI units) Allowable Strength Design (SI 단 위 계) Load and Resistance Factor Design (US units) Allowable Strength Design (US u nits) Load and Resistance Factor Design (SI units)

AISC360-05M(ASD)

Allowable Strength Design (SI units)

AISC-ASD89

Allowable Strength Design

EN1993-1-1-2005

Limit State Design

EN1993-1-1-1992

Limit State Design

BS5950-1-1990

Limit State Design

KSSC-LSD09

Load and Resistance Factor Design

Section 1. Outline | 41

DESIGN REFERENCE


KSSC-ASD03


AIK-ASD83


The program supplies a design summ ary of the calculations for all the design criteria shown in Table 2.1.1. Detailed calculations for the mo st widely used design codes (AISC360-10(LR FD) / AISC36010(ASD) / AISC360-10M(LRFD) / AISC360-10M(ASD) / AISC ASD89 / KSSC-LSD09 / KSSC-ASD03) are provided as well. In the detailed design report, the user may also see specific design code details or basis for the d esign calculations.

42 | Section 1. Outline


DESIGN REFERENCE

Figuree 2.1. Figur 2.1.11 Member Design

Result>Design Result>Design Report

Report set up dialog window

Sect Se ctio ion n 1. Ou Outl tlin ine e | 43

DESIGN REFERENCE

Figure Fig ure 2.1 2.1.2 .2 Sampl Samplee Design Summary Report

44 | Se Sect ctio ion n 1. Ou Outl tline ine


DESIGN REFERENCE


Design Figuree 2.1. Figur 2.1.33 Samp le Design Detail Report

Sect Se ctio ion n 1. Ou Outl tlin ine e | 45

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46 | Se Sect ctio ion n 1. Ou Outl tline ine


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DESIGN REFERENCE

The design code may be set in Home>Design Settings>General>Design Code . When the country code is selected, the available design codes w ill be shown .

Figure 2.1.4 Design Code

The program also offers a material database for steel, and each database applies different tensile strengths and yield strengths to the design.

ASTM/ASTM09 (미국 ), BS/BS04 (영국 ), CNS/CNS06 (대만 ), CSA (캐나다 ), DIN (독일) EN/EN05-PS/EN05-SW/EN05 (유럽 ), GB/GB03/GB12/JGJ/JTG04/JTJ/TB05 (중 국) GOST-SNIP/GOST-SP (러시 아), IS (인도), JIS-Civil/JIS (일본 ), UNI (이탈리 아) KS-Civil/KS08-Civil/KS08/KS09/KS10-Civil/KSCE-LSD12 (한국)


DESIGN REFERENCE


Figure 2.1.5 Material set up dialog window

The design of steel cross sections may be based on a pre-defined cross section template, modified cross section after selecting one from the template database, or a cross-section based on a useruploaded DWG file. When the cross section comes from a template, the cross section shape that is included in the design code follows said code. If it is a sha pe that is not included in the selected design code, it is overridden with a shape that is included in the code before proceeding with design 52 | Section 1. Outline

DESIGN REFERENCE


computations. Shapes that cannot be overridden may be used in the design by setting the typical cross se ction material strength redu ction factor or effective design reduction factors.


DESIGN REFERENCE


The o verriding procedure for cross sections that were selected from a cross se ction temp late is shown below.

Table 2.1.2 Overriding the shapes of cross s ections chosen from template designs

Double Angle

-

Double Angle (T)

Back

Double Channel (H)

Face

Box

-

Box

Double Channel

Double H-Section 2H Combined Shape

Vertical

3H Combined Shape

-

H-Shape with Flange Plate Biaxial H-Shape

Downward

H

Upward

H

Vertical

H-Shape with Flange Plate

-

H-Shape with Flange Plate

-

Box

H-C Combined Shape

H-T Combined Shape H-Shape with Flange Plate H-Shape with W eb Plate 2T Combined Shape 4-Angle


Face -

H Box

DESIGN REFERENCE



DESIGN REFERENCE


General section strength check design factors may be input for either all applicable members or a specific me mber in the following dialog window.

Hom e>De sign Settings>G eneral>Design Code> Steel>Code-Specific Steel Design Parame ters Figure 2.1.6 Steel Design Parameters dialog window


DESIGN REFERENCE


Analysis & Design>Analysis & Design>Member Parameters Figure 2.1.7 Member Design Parameters dialog window


DESIGN REFERENCE

S e c t io n 2


Design F actors – AISC360-10 Strength Reduction Factor / Safety Factor This section explains the selection of strength reduction factors and safety factors for tension, compression, bending, shear, and torsion. If the load and resistance factor design (LRFD) m ethod is being used, then strength reduction factors are selected, and if the allowable strength design (ASD) method is being used, then safety factors are selected. Recommended industry values are used as program default values, and the user may modify these values. The factors are selected and applied to the entire model.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters Figure 2.2.1 Strength reduction factor (LRFD) / safety factor (ASD ) set up (LRFD)

(ASD)

Setting Lateral Bracing for all Beams and G irders This section discusses how to select criteria for lateral bracing of beam s and girders. After selecting “considered” for lateral bracing, lateral-torsional buckling failure mode is not considered.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters Figure 2.2.2 Beam/Girder Lateral Bracing set up dialog window for the entire model

58 | Section 2. Design Factors – AISC360-10


DESIGN REFERENCE

Lateral torsional buckling criteria may be set for each member. To enter the unbraced length, the lateral unbraced length (L b ) should be checked. Then, the user may specify an unbraced length for that member.

Analysis & Design>Analysis & Design>Member Parameters>Unbraced Length Figure 2.2.3 Member-specific unbraced length set up dialog window

Moment Magnifiers The en tire structure or a spe cific mem ber may b e subject to 2 nd order effects (P-Δ, P-δ effects) and to incorporate such effects, second order analysis may be approximated by using first order analysis results and a moment m agnifier.

Figure 2.2.4 P-δ Effect

Section 2. Design Factors – AISC360-10 | 59

DESIGN REFERENCE


B 1 is a magnification factor that incorporates P-δ effects that may occur due to member strains. This program offers automatic calculation of this magn ification factor and is computed as follows: B1 =

C m a P r

1-

(2.2.1)

P e1

Here, α

= 1.0 (L RFD ), 1 .6 (A SD )

Cm

= Factor assum ing no lateral displacement of the frame With no lateral loads, C m = 0.6 - 0.4

M 1 M 2

With lateral loads, C m = 1.0 P e1 =

p 2 EI *

( K 1 L) 2

P r = P nt + B2 P lt

B 2 is a magn ification factor that incorporates P-Δ effects due to displacement along the length between two po ints on a mem ber, and is computed as follows: B2 =

1 ³1 P story 1 - a P e story

(2.2.2)

Here, α

= 1.0 (LRFD), 1.6 (ASD)

P story

: Total vertical load carried by the story

P e story

: Elastic buckling strength of the story belonging to the laterally unbraced fram e

Howe ver, this program does not supp ort automatic computation of the B2 magn ification factor. Thus, if the user does not specify a value for B2, a default value of 1.0 is used. To consider m ore accurate 2 nd order effects, results from P-Δ ana lysis may be used in design.


DESIGN REFERENCE


The moment magnifiers may be automatically computed for the entire model. For specific members, the mo ment m agnifier factors can either be automatically computed or specified by the user.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters Figure 2.2.5 Dialog window showing mom ent magnifier automatic comp utation

Analysis & Design>Analysis & Design>Member Parameters>Moment Magnifier Factor Figure 2.2.6 Dialog window showing mom ent magnifier selection for a specific


DESIGN REFERENCE


Lateral Torsional Buc kling M odification Factor If the beam is not subject to distributed momen t, nominal bending strength is computed as the produ ct of the basic strength and the lateral torsional buckling modification factor C b . C b is computed according to Equation 2.2.3, and can be assum ed to be 1.0 a s a conservative estimate. C b =

12 .5 M max 2.5 M max + 3 M A + 4 M B + 3 M c

(2.2.3)

Here, M m ax

= Abso lute value of the maximum m oment in the unbraced length

MA

= Abso lute value of the mom ent at a quarter length along the unbraced length

MB MC

=

Absolute value of the mom ent at halfway along the unbraced length

= Abso lute value of the mom ent three quarters length along the unbraced length

The lateral-torsional buckling factor ma y be computed automatically for the en tire m odel. For specific memb ers, either the automated o r user-specified values may be used.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters Figure 2.2.7 Dialog window for setting up the lateraltorsional buckling factor for

Analysis & Design>Analysis & Design>Member Parameters>Lateral Torsional Buckling Moment Figure 2.2.8 Dialog window

Coefficient

for setting up the lateral torsional buckling factor for a


DESIGN REFERENCE



DESIGN REFERENCE


Web Shear Coefficient Web shear coefficient or shear buckling reduction factor C v is used in conjunction with material strength when com puting the nominal shear strength, and is computed base d on the ratio of the web’s depth and thickness. Except for circular hollow sections, all dual-axis symm etry cross sections, single-axis symmetry cross sections, and C-shape sections are divided into the three categories shown below in Figure 2.29 to compu te the shear buckling reduction factor.

Figure 2.2.9 Web Shear Coefficient

In each section, the calculation for C v is as follows.

T a bl e 2 .2 .1 C v equations for

Condition

each condition

h / t w £ 1.10 k v E / F y 1.10 k v E / F y < h / t w £ 1. 37 k v E / F y


Cv C v = 1. 0

C v =

V n based on Shear yielding

1.10 k v E / F y h / t w

Buckling


DESIGN REFERENCE

h / t w > 1.37 k v E / F y

C v =

1.51 Ek v

( h / t w ) 2 F y

Elastic buckling

However, for sections w ith h / t w £ 2.24 E / F y or rolled H-shape webs, C v = 1.0.

For the entire model, the web shear coefficient may be computed automatically. For individual memb ers, either the automated va lues or user-specified values may be u sed.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters Figure 2.2.10 Dialog window for setting the w eb shear coefficient for the entire

Analysis & Design>Analysis & Design>Member Parameters>Web Shear Coefficient Figure 2.2.11 Dialog window for setting the w eb shear coefficient for a specific


DESIGN REFERENCE

S e c t io n 3


M em ber Exam ination P rocedure

–

AISC360-10 The steel member examination procedure following the AISC360-10 design code is as follows.

Load combination or design strength modification factors are applied to the analyzed strengths, and the various strengths are calculated based on the design code and then checked for safety. In particular for beam members, the program will check for sag, and for repeated loads (such as crane girders), fatigue checks w ill also be conducted.

66 | Section 3. Member Examination Procedure – AISC360-10


DESIGN REFERENCE

Calculation of Design Demand s Design deman ds/forces are computed by applying load combinations, live load reduction factors, and mome nt mag nification factors to the an alyzed strengths.

1) Applying load combinations The analyzed dem ands at the mem ber check points, load types, and the load combination factors are incorporated in compu ting the design dema nds.

2) App lying the live load redu ction factor As explained in the section Design Factors>Live Load Reduction Factors, compone nts that are subject to live loads will have design forces that incorporate the live load reduction factor.

3) Applying the moment ma gnifier

Section 3. Member Examination Procedure – AISC360-10 | 67

DESIGN REFERENCE


The following equation describes how to compute the second order moment and axial force incorporating the first order strength and moment magnifier. In the case of axial force, the following equation is only applied for co mpressive forces.

M r = B1 M nt + B 2 M lt P r = P nt + B 2 P lt

(2.3.1) (2.3.2)

Here, M nt

= 1 st order mo ment wh en there is no lateral deflection of the structure. In this program, this mome nt is due to dead and live loads.

M lt

= 1 st order mo ment w hen there is lateral deflection of the structure. In this program, this mom ent is due to all loads except for dead and live loads.

P nt

= 1 st order axial force w hen there is no lateral deflection of the structure. In this program, this force is due to dead and live loads.

P lt

= 1 st order axial force when there is lateral deflection of the structure. In this program, this force is due to all loads except dea d and live loads.

Calculation of Design Strengths The design strength of each mem ber is based on load combinations and must be greater than the calculated required strength.

(LRFD)

(2.3.3)

W (ASD)

(2.3.4)

R u £ f R n

Ru £

Here, Ru

: Required strength

Rn

: Nominal strength


Rn


DESIGN REFERENCE

Φ

: Str en gt h re du ctio n fa cto r

Ω

: Safety factor

1) Axial strength: Tension members Members subject to tension about the central axis must undergo checks regarding slenderness ratio limits and design e longation/tensile strengths.

Slenderness ratio limits for tension me mbers are created to limit sagging or vibration due to self weight. Moreove r, if the tension m embe rs are too flexible, the mem ber ma y be twisted severely in the process of transportation or construction. As a result, proper examination is recomme nded. The default recomm ended limit is 300, but the user m ay specify an alternative value. L r

£ 300

(2.3.5)

The no minal strength of a tension me mber is typically set to be the minimum of the gross section yielding limit state and the effective cross section yielding limit state. However, this program does not support conne ction d esigns and thus the yield limit state for only the gross cross section is calculated. P n = F y A g

(2.3.6)

2) Axial strength: Compression mem bers Members subject to compression about the central axis must undergo checks regarding slenderness ratio limits and design com pressive strengths.


DESIGN REFERENCE


Unlike tension members, the slenderness ratio limits for compression members incorporate an effective length factor K. The default recommended slenderness ratio limit is 200, but the user may specify an alternative value.

KL r

(2.3.7)

£ 200

For compression mem bers, long and slender elements incorporate the reduction factor Q=Q sQ a when calculating the design compressive strength. To do this, the cross section must be properly categorized using the width to thickness ratio. The nom inal strength of a compression member, depending on the cross-section shape, is selected to be the minimum of the flexural buckling (FB) limit state, torsional buckling (TB) limit state, and the flexural-torsional buckling (FTB) limit state.

(2.3.8)

P n = F cr A g

Table 2.3.1 Limit states

Limit State

depending on the crosssection shape

Cross-Section Shape

Compact/Noncomp act Section


Slender Se ction


DESIGN REFERENCE

FB TB

FB FTB

FB

Asymm etrical shapes (except for L-shaped

LB FB TB LB FB FTB LB FB

FB

FB

FTB

FTB

FB

N/A

FTB

sections)

LB FTB

FB=flexural buckling, TB =torsional buckling, FTB= flexural-torsional buckling, LB =local buc kling

For a typical cross section, F cr is the product of the steel yield strength F y and the typical section material strength reduction factor. The nominal comp ressive strength is calculated as follows. P n = ( Material Strength Factor ) ´ F y A g

(2.3.9)

3) Flexural/Bending Strength Nominal flexural strength is determined based on the member’s width to thickness ratio and the laterally unbraced length. Moreover, various limit states depending on the section’s shape or flexuralcompressive memb er’s cross-section category (compa ct, noncomp act, slender) are also examined, and the minimum va lue of those limit states is used.


DESIGN REFERENCE


The nominal flexural strength of a member and how it is a function of the width to thickness ratio is shown in Figure 2.3.1. As shown below, the calculation may be split into three areas of compact, noncompact, and slender members. As the width to thickness ratio increases, the nominal flexural strength decreases. Figure 2.3.1 Nom inal flexural strength based on the w idth to thickness ratio

The no minal flexural strength of a m ember a nd how it is a function of the mem ber’s laterally unbraced length is shown below in Figure 2.3.2. The comp utation may be split into four areas of plastic design, full plastic, inelastic lateral buckling, and elastic lateral buckling. As the laterally unbraced length increases, the nom inal flexural strength decreases. Figure 2.3.2 Nominal flexural strength based on the mem ber’s laterally unbraced



DESIGN REFERENCE

If the beam is not subject to distributed moment, the nominal flexural strength is computed as the product of the b asic strength and the modification factor C b . For typical cross-sections, the nom inal flexural strength, such as in the case of comp ression mem bers, the material strength reduction factor of typical cross-sections is incorporated into the calculation. M n = ( Material Strength Factor ) ´ F y Z

(2.3.10)

Here, Z = Plastic section modulus about the deflection axis.

4) Shear Strength

The nom inal shear strength of the web is comp uted as follows, depending on the cross-section shape.

Table 2.3.2 Nominal shear strength of webs depending

Cross-Section Shape

Nominal Shear Strength V n

Shear Area A w

on the cross-section shape Section 3. Member Examination Procedure – AISC360-10 | 73

DESIGN REFERENCE


Single- or dual-axis symmetry members, channel shapes’ webs L-shape cross-sections Square-shape or box-shape hollow section Circular hollow section Minor axis of single- or dual-axis symmetry members

V n = 0 .6 F y Aw C v

Aw = bw hw

V n = 0 .6 F y Aw C v

Aw = bt

V n = 0 .6 F y Aw C v

Aw = ht

V n = F cr A g / 2

V n = 0 .6 F y Aw C v

Aw = b f h f

For typical cross sections, the nom inal shear strength incorporates the effective shea r area factors and is calculated as follows: V n = ( Material Strength Factor ) ´ F y ´ ( Effective Shear Area Factor ) ´ As

(2.3.11)

5) Torsional S trength Steel tube sections can better resist torsion compared to open type cross sections. Thus, the torsional strength is compu ted with the assump tion that the total torsional moment is resisted by the pure torsion shear stress. For other cross-sections, the minimum value is selected from the vertical stress yielding limit state, shear stress yielding limit state, and the buckling limit state. In AISC 360-10, torsional strength equations are provided only for steel tube cross sections, so this program also supports torsional checks for steel tube cross se ctions.



DESIGN REFERENCE

6) Com bination Strength Ratios In cases where the member is subject to both lateral and axial loads, the following interaction equations mus t be satisfied:

 ≥ 0.2 :  + 9  +   < 0.2 : 2 +  + 

(2.3.12)

(2.3.13)

In particular, tensile loads can increase the flexural strength, and thus wh en calculating M c, C b should be m ultiplied by

1+

P r P ey

and then applied to the interaction equations..

Members subject to torsion, flexure, shear, and axial force simultaneously must satisfy the following interaction equation. According to AISC 360-10, torsional strength equations are only provided for box or pipe shape cross sections, and as a result the program ch ecks for torsional strength for only box or pipe shape cross sections.

T r £ 0 .2T c

: Neglecting torsional effects

          > 0.2 :  + + + 

(2.3.14)

(2.3.15)


DESIGN REFERENCE


Serviceability Ch ecks All of the structure, including each specific structural member and connections, must be checked for serviceability. When p erforming this check, the load factors in load combinations are a ll 1.0. However, the factor for earthquake loading is 0.7.

1) Sagging Checks Excessive sagging has negative effects on the structure’s appearance and performance. It may also cause damage to nonstructural components, and thus the actual deflection must be smaller than the allowable deflection.

d actual £ d allow

(2.3.16)

The actual deflection is calculated as the product of the load combination factor and the analyzed deflection value. The allowable deflection is based on the member length and the user-specified design environment.

Fatigue Checks If there are repeated loads on a structure, it may experience fatigue and cracks may occur. If cracks become enlarged, the structure may experience collapse. Such fatigue effects are caused by a large numbe r of repeated stresses, and is not typically applied to building structures. Crane girders that are subject to repeated loads or structures that resist machinery or equ ipment ma y, however, experience cracks


due

to

fatigue.


DESIGN REFERENCE

S e c t io n 4

De sign Param eters EN1993-1–

1:2005 Partial Factor This section explains how to select and app ly partial factors for the cross-section ultimate limit value (γ M0 ), partial factors for instability checks for individual members (γ M1 ), and partial factors for resistance limit value (for tensile rupture) (γ M2 ). Industry recommen ded values are used as default values in the software, but the user may modify these values. The specified pa rtial factors are applied to the entire model.

Home>Design Settings>General>Design C ode>Steel>Design Co de-Specific Steel Design Parameters Figure 2.4.1 Dialog window for setting the partial factor

Setting Lateral Bracing for all Beams and G irders This section explains how to set the lateral bracing conditions for all beams and girders in a model. The user can select “Considered” for “All Beams/Girders are Laterally Braced”, in which case the lateral-torsional buckling strength is not considered.

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters

Section 4. Design Parameters – EN1993-1-1:2005 | 77

DESIGN REFERENCE


Figure 2.4.2 Dialog window for setting lateral bracing conditions for all beams a nd

The condition for not considering the lateral-torsional buc kling strength can b e specified for individual members. In setting the member parameters, when the “Lateral Unbraced Length” option (or L b ) is checked o ff, the program will consider this mem ber to be laterally unbraced.

Analysis & Design>Analysis & Design>Member Parameters>Unbraced Length Figure 2.4.3 Dialog window for setting the unbrac ed length for a specific membe r

78 | Section 4. Design Parameters – EN1993-1-1:2005


DESIGN REFERENCE

Equivalent Uniform Mom ent Factor When calculating the buckling strength of a member subject to both compression and bending, the interaction factors k yy , k yz , k zy , k zz , must first be computed. In doing so, equivalent uniform momen t factors are required. The equivalent uniform moment factors for each direction (either for lateral buckling or lateral-torsional buckling) are computed as follows.

Table 2.4.1 Equivalent uniform mom ent factors for each direction, based on

 ̅    ≤ 0.2  1−  1− 

 

 ̅    > 0.2  1−  1− 

 = = +1−   1− ,1− , 

Here, l 0 : Dimensionless slenderness ratio based on lateral-torsional buckling due to uniform mom ent C 1 : This is defined based o n the loading and e nd cond itio ns. It may b e calculated as C 1 = k c-2 .

k c is a mo dification factor and is computed as follows.


DESIGN REFERENCE


Table 2.4.2 Moment

Moment distribution

distribution shapes and the

k c

corresponding modification

1. 0  =  1 1.33 − 0.33

− ≤  ≤ 

0.94

0.90

0.91

0.86

0.77

0.82

N cr , y , N cr , z : Elastic flexural buckling stress for the major and minor axes N cr ,T

e y

►

: Elastic torsional buckling stress

is calculated based on the cross-section class type.

Class 1, 2, 3 : e y =

►

Class 4

:


M y, Ed A N Ed W el , y

(2.4.1)


DESIGN REFERENCE

e y =

M y , Ed Aeff N Ed W eff , y

(2.4.2)


DESIGN REFERENCE


C mi,0 is calculated in each directio n as sho wn below .

Table 2.4.3 C mi,0 in each

direction

The equivalent uniform moment factor can be automatically computed and then applied to the entire model. For individual members, the automated value may be used, or the user may specify an alternative value.

Figure 2.4.4 Dialog window

Home >De sign Settings>G eneral>Design Code> Steel>Design Code-Specific Steel Design Parame ters

for setting automation for the equivalent uniform mom ent

Analysis & Design>Analysis & Design>Member Parameters>Equivalent Uniform Moment Factors for FB Figure 2.4.5 Dialog window for setting equivalent uniform mom ent factors for individual



DESIGN REFERENCE

Analysis & Design>Analysis & Design>Member Parameters>Equivalent Uniform Moment Factors for LTB Figure 2.4.6 Dialog window for setting equivalent uniform mom ent factors for individual


DESIGN REFERENCE

S e c t io n 5


M em ber Exam ination P rocedure

–

EN1993-1-1:2005

Calculating D esign Strength The design strength is calculated by incorporating load combinations and live load reduction factors into the analyzed strengths.



DESIGN REFERENCE

1) Load Combination Factors The de sign strength is comp uted by incorporating the ana lyzed strengths at the m ember chec k points, load com bination types, and the load combination factors.

2) Live Load Reduction Factors As men tioned in the Section De sign Factors > Live Load Reduction Factors, only the me mbers subject to live loads w ill incorporate live load reduction factors for computation of design strength.

Ultimate Limit State The design resistance value of the cross-section must be greater than the design load values, and an important factor in calculating the re sistance va lue is the cross-section classification. The E urocode categorizes cross-sections into four classes and the de finitions for each class a re shown below.

Table 2.5.1 Cross-sections categorized according to the

Class 1

Class 1 cross-sections are those which can form a plastic hinge with the rotation capacity required from plastic a nalysis w ithout reduction of the resistance.

Class 2

Class 2 cross-sections are those which can develop their plastic moment resistance, but have limited rotation cap acity because o f local buckling.

Eurocode

Class 3

Class 4

Class 3 cross-sections are those in which the stress in the extreme compression fibre of the steel membe r assum ing an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance. Class 4 cross-sections are those in which local buckling will occur before the attainment of yield stress in one or more parts of the cross-section.

Figure 2.5.1 Cross-Section Classification according to Eurocode 3


DESIGN REFERENCE


1) Axial strength: Tension Members Memb ers sub ject to uniform tension must s atisfy the following limit state: N Ed N t , Rd

£ 1.0

(2.5.1)

The design strength for tension members is selected to be the minimum of the gross section design plastic resistance strength and the net section design ultimate resistance strength. However, the program only considers the gross section design plastic resistance strength.

N pl , Rd =

Af y g M 0

(2.5.2)

2) Axial strength: Compression Mem bers Memb ers subject to uniform comp ression must satisfy the following limit state: N Ed £ 1.0 N c, Rd


(2.5.3)


DESIGN REFERENCE

The design strength for compression membe rs, N c,Rd , is calculated using either the gross section area or the effective section area depend ing on the section class. The equations are shown below.

►

C lass 1, 2, 3 : N c, Rd =

►

Class 4

Af y

(2.5.4)

g M 0

: N c , Rd =

Aeff f y

(2.5.5)

g M 0

3) Lateral Strength Memb ers sub ject to pure lateral loads must satisfy the following limit state. M Ed M c , Rd

►

£ 1.0

(2.5.6)

Class 1, 2 :


DESIGN REFERENCE


,   ►

Class 3

(2.5.7)

:

,, = ,  ►

Class 4

(2.5.8)

:

, , 

(2.5.9)

4) Shear Strength Memb ers sub ject to shear forces mu st satisfy the following limit state. V Ed V c, Rd

(2.5.10)

£ 1.0

Design shear strength V c,Rd is calculated using the following equation using the design plastic shear strength (where torsion does not exist):

V c, Rd = V pl , Rd =

(

)

Av f y / 3 g M 0

(2.5.11)

In the above equation, design cross-section area A v is calculated using different equations for different cross-section shapes .

Table 2.5.2 Calculation of design section area A v depending on the cross-

Rolled I, H shapes

W eb

Av = A - 2 bt f + (t w + 2 r )t f £ h hw t w

Rolled C shapes

W eb

Av = A - 2bt f + (t w + r )t f



DESIGN REFERENCE

Rolled T shapes

W eb

Av = A - bt f + (t w + 2 r )

W elded T shapes

W eb

Av = t w çç h -

Welded I, H shapes,

W eb

Av = h

Rectangular sections

Flange

æ

height

rectangular hollow section

Section depth

Uniform thickness circular hollow se ction

-

÷

2 ø÷

å (h t ) w w

Av = A -

å (h t )

Av = A

h

Av = A

Av =

2

t f ö

è

Section Uniform thickness

t f

w w

b+h b b+h

2 A p


DESIGN REFERENCE


5) Comb ined Strength Whe n a me mber is subject to both lateral and shear forces, the lateral strength may be reduc ed if the shear force is large. If the shear force is greater than h alf of the plastic shear s trength, then the lateral strength is calculated by redu cing the material’s yield strength.

V Ed >

1 2

V pl , Rd : When calculating lateral strength, (1- ρ)fy is used instead of fy 2

1 V Ed £ V pl , Rd 2

æ 2V ö r = ç Ed - 1÷ ç V pl , Rd ÷ è ø : Calculation of lateral strength without any reductions due to shear force

When a member is subject to both lateral and axial forces, the member must satisfy the following equations based o n its cross-section class. ►

Class 1, 2 : Design plastic lateral strength is reduced due to ax ial force M Ed £ M N , Rd

►

Class 3

: Cons ideration of the peak axial stress limit due to lateral and axial forces

s x, Ed £ ►

Class 4

(2.5.12)

:

f y g M 0

  , + , ≤ 1  + / ,,/ ,,/

6) Buckling strength verification – axial lo ad Memb ers sub ject to axial force m ust satisfy the following eq uation for buckling b ehavior:


(2.5.13)

(2.5.14)


DESIGN REFERENCE

N Ed N b, Rd

N Ed

Howe ver, if l £ 0.2 or N cr

£ 1.0

(2.5.15)

£ 0.04 , buckling effects may be n eglected.

Design buckling strength N b,Rd for an axial mem ber is calculated as follows.

►

Class 1, 2, 3 : N b, Rd =

►

Class 4

c Af y g M 1

(2.5.16)

: N b, Rd =

c Aeff f y g M 1

(2.5.17)

7) Buckling strength verification – lateral load If a member that is laterally unbraced is subject to bending about the strong axis, the member must satisfy the following equation regarding lateral-torsional buckling: M Ed M b, Rd

£ 1.0

(2.5.18)


DESIGN REFERENCE


However, if the member is a beam and its compressive flange is sufficiently supported, or if the memb er cross-section is a square or circular hollow section, lateral-torsio nal b uckling is not considered. Furthermore, if l LT £ l LT , 0 or M Ed £ l LT ,02 , lateral-torsional buckling m ay also be neglected. M cr

Design buckling mom ent is calculated as shown below.

►

C la ss 1, 2 : M b , Rd = c LT W pl , y

►

Class 3

Class 4

g M 1

(2.5.19)

: M b , Rd = c LT W el , y

►

f y

f y g M 1

(2.5.20)

: M b, Rd = c LT W eff , y


f y g M 1

(2.5.21)


DESIGN REFERENCE

8) Buckling strength of a mem ber subject to both axial and lateral loads

Depending on the cross-section class, N R k, M y,Rk , M z,Rk, ΔM y,Ed , ΔM z,Ed are calculated differently, as shown below.

Table 2.5.3 Calculating

N Rk = f y Ai

(2.5.22)

M i, Rk = f yW i

(2.5.23)

Class

1

2

3

4

Ai

A

A

A

Aeff

W y

W pl , y

W pl , y

W el , y

W eff , y

W z

W pl , z

W pl , z

W el , z

W eff , z

D M y , Ed

0

0

0

e N , y N Ed

D M z , Ed

0

0

0

e N , z N Ed

N R k , M y , R k , M z , R k based on the cross-section class


DESIGN REFERENCE


Lateral buckling reduction coefficients c y , c z are calculated with different parameters for each direction. 1

c =

2

(2.5.24)

£ 1.0

F + F - l 2

Here,

[

F = 0.5 1 + a ( l - 0.2 ) + l

2

]

l : dimensionless slenderness ratio

►

Class 1, 2, 3: Af y

l = ►

(2.5.25)

N cr

Class 4: l =

Aeff f y

(2.5.26)

N cr

a : Imperfection factor for the buckling curve Table 2.5.4 Imperfection factor a for the buckling curve

Buckling curve Imperfection factor

a

a0

a

b

0.13

0.21

0.34

d 0.49

0.76

N cr : Elastic critical force.

The lateral-torsional buckling reduction coefficient c LT is calculated as follows.

c LT =

Here, 2 F = 0.5éê1+ a l - 0.2 + l ùú ë û

(

)


1 2 LT

F LT + F LT - l 2

£ 1.0

(2.5.27)


DESIGN REFERENCE

l LT =

W y f y M cr


DESIGN REFERENCE


a LT : Imperfection factors for the lateral-torsional buckling curve

Buckling curve Imperfection factor

a

a

b

0.21

0.34

d 0.49

0.76

M cr : Elastic critical mom ent

Interaction factors k yy , k yz , k zy , k zz may be calculated using either Annex A or Annex B. midas Plan uses equations of Annex A.

Table 2.5.5 Calculation of interaction factors – Annex A

Design assumptions Interaction factors

Elastic cross-sectional properties class 3, class 4

 1− ,  1− ,  1− ,  1− ,

k yy

k yz

k zy

k zz

 1− 1 ,  1− 1 0.6  ,  1−  1 0.6  ,   1− 1 ,

Memb ers sub ject to both axial and lateral loads mu st satisfy the following interaction equations.

  + , +,, + , +, ,     96 | Section 3. Member Examination Procedure – AISC360-10

(2.5.28)

DESIGN REFERENCE


  + , +,, + , +, ,    

(2.5.29)


DESIGN REFERENCE


Serviceability Limit State It is important to verify the serviceability of the entire structure, each individual member, connections, and joints. When checking for serviceability, the load factor used in all load co mbinations is set to be 1.0 (the load factor for earthquake loading is set to be 0.7).

1) Deflection Checks Excessive deflection negatively affects the structure’s appearance and performance. It can also damag e the nonstructural componen ts. Thus, the actual deflection must be smaller than the allowable deflection.

d actual £ d allow

(2.5.30)

The a ctual deflection is the product of the analyzed deflection and the load comb ination factors. The allowable deflection is calculated using the user-specified ratio to b e applied to the mem ber length. The E urocode checks for the b eams’ vertical deflection and the columns’ horizontal deflection.

Fatigue Checks If there are repeated loads on a structure, it may experience fatigue and cracks may occur. If cracks become enlarged, the structure may experience collapse. Such fatigue effects are caused by a large numbe r of repeated stresses, and is not typically app lied to bu ilding structures. Crane girders that are subject to repeated loads or structures that resist machinery or equ ipment ma y, however, experience cracks


due

to

fatigue.

DESIGN REFERENCE


Section 5. Member Examination Procedure – EN1993-1-1:2005 | 99

DESIGN REFERENCE

S e c t io n 6


Cross-Section C om putations In this program, mem ber strength and the user-specified control data is used to create the steel crosssections. However, the cross-sections must satisfy the criteria shown below.

Table 2.6.1 Domain of available steel cross-sections for midas nGen

Cross-Section Shape

Cross-Section DB

H Shape

All DB

C Shape

All DB

L Shape

All DB

T Shape

All DB

Rectangular Hollow

All DB

Section Circular Hollow Section

All DB

2 L S ha pe

AISC2K(US), AISC2K(SI), AISC, CNS91, BS4-93, GB-YB05

Steel Section Calculation Se t Up When the design process begins, the dialog window shown below will appear. When Design Calculation Option>Steel Se ction is Checked-On , then the program w ill find sections that satisfy the

memb er strength and other criteria, which will then be reflected in the mo del and a fterwards the d esign calculations w ill be repeated.

Figure 2.6.1 Run Design dialog window

100 | Section 6. Cross-Section Computations


DESIGN REFERENCE

The u ser may click the [… ] button to access more detailed design settings to mod ify section criteria. Depen ding on the mem ber type design group, the section’s depth and height ranges may be specified.

Figure 2.6.2 Design Settings for Steel Section dialog window

In the case of steel mem bers, a more efficient sectio n ma y be found by b rowsing the candidate section list. To access this, the user m ay press the Detail Setting button. The user ma y then select the target candidate sections from e ither the D B or u ser-specified sections. Section 6. Cross-Section Computations | 101

DESIGN REFERENCE


Figure 2.6.3 Detail Setting dialog window

Steel Section Ca lculatio n P rocess After modeling and analysis, the steel section calculation process is as shown below. Figure 2.6.4 Steel m ember section calculation process



DESIGN REFERENCE

1) Calculate the design demands Calculate the design demands by applying the load combination and design code modification factors.

2) Find load combination envelopes for each comp onent midas nGe n does not go through the section calculation process for all load combinations. The program finds the load combination that yields the maximum and minimum values of the member’s axial, shear, torsional, and lateral demands, in order to find the design with the largest possibility of becoming the governing design. Shear and moment demands must also consider both the major and minor axe s, and thus a total of 12 load com binations is required for proper section calculation.

P m ax

V y,max

V z,max

T m ax

M y,max

M z,max

P

Section 6. Cross-Section Computations | 103

DESIGN REFERENCE




DESIGN REFERENCE

3) Calculate target strengths from the de sign strengths for each compo nent To satisfy the inequality (Design demand) ≤ (Design strength) X (Target ratio), the target strengths are calculated for each compo nent of the internal member forces and design deman ds.

4) Calculate target stiffnesses from the target strengths for each co mponen t The target stiffnesses are co mputed from the target strengths for each force com ponent. Table 2.6.2 Equations for calculating the stiffnesses

Force component

Calculation of Stiffness

Axial (Tension)

Atar =

Axial (Compression)

Atar =

Shear

Av,tar =

Moment

S tar =

from target strengths

P Target Ratio ´ 0.7 ´ F y

P Target Ratio ´ 0.7 ´ F y V Target Ratio ´ 0.7 ´ F y M Target Ratio ´ 0.7 ´ F y

5) Sea rch for the most e ffective cross section con sidering the target stiffness an d dep th limitations for each component The ratio o f the calculated target stiffness to the a ctual stiffness is calculated, and is used to determine whether the section is adequate or not (‘OK’ or ‘NG’, respectively). Based on this result, the most effective section is chosen from the sections deemed ‘OK’ from the user-specified section list. Moreover, the height and depth ranges set in Design Setting will be incorporated in the final cross section, and thus the m ost econom ic and efficient section will be chosen.

Table 2.6.3 Ratios to check design adequacy for each force component

Force component Axial (Tension)

Axial (Compression)

Ratio for checking design adequacy Ratio =

Atar 0.6 A g

ì 0.877 ï 2 Factor = í l c ï0.658l î

2 c

( l c > 1.5) ( l c £ 1.5)

Section 6. Cross-Section Computations | 105

DESIGN REFERENCE


Ratio =

Shear

Ratio =

Moment

Ratio =

Atar Factor ´ A g Av ,tar 0.8 Av S tar S

6) Section Update/Re-Analysis After completing the steel calculations, a re-analysis is required if the cross-section has changed (as this will change the structure’s strength distribution). After updating the section, analysis should be repeated and the cross section should be checked for adequacy before outputting the final design results.


Chapter 3. RC Design

DESIGN REFERENCE

S e ctio n 1

Outline Reinforced concrete (RC) m embers that are included in the analysis model are checked for adequate strength and rebar arrangem ents based o n user-specified criteria or on the entire RC structure.

The program offers the following design codes.

Table 3.1.1 Design codes

ACI318-11

Ultimate Strength Design

categorized per country

ACI318-08


ACI318-05


ACI318-02


ACI318-99


ACI318-95


ACI318-89


EN1992-1-1:2004

Limit State Design

EN1992-1-1:1992

Limit State Design

BS8110-1997

Limit State Design

KCI-USD12


KCI-USD07


KCI-USD03


KCI-USD99


The program supplies a design summary of the calculations for the design criteria shown above. Detailed calculations for the criteria below a re also provided.


DESIGN REFERENCE



►

ACI318-11

►

KCI-USD12


DESIGN REFERENCE

The design code may be set in Home>Design Settings>General>Design Code . When the country code is selected, the available design codes w ill be shown .

Table 3.1.1 Design Code

The program also offers a material database for concrete, and each database applies different compressive strengths to the design.

ASTM (US), BS (UK), CNS /CNS560 (TW), CSA (CA), EN/EN04 (EU), GB/GB10/GB-Civil/JTG04/TB05 (CN), GOST-SNIP/GOST-SP (RU), IS (IN), JIS-Civil/JIS (JP), UNI/NTC0 8/NTC12 (IT) KS-Civil/KS/KS01(KCI-2003)/KS01(KCI-2007)/KS01(KCI-2012)/KS01-Civil(KCI-2003)/ KS01-C ivil (KCI-2007)/KS01-C ivil(KCI-2012)/KSCE-LSD12 (KR )


DESIGN REFERENCE


Figure 3.1.2 Material and section set up dialog window

The R C se ction may be selected to be either rectangular or round using the section template capability. Beams may only be rectangular, but column/braces may have rectangular or round sections.



DESIGN REFERENCE

S e ctio n 2

Rebar/Arrangement This section explains how to set the rebar/arrangement information, such as rebar type, diameter, spacing, and covering thickness. This can be done in Home>Design Settings>Rebar/Arrangement .

Rebar Material This program offers the following rebar m aterial databases.

ASTM (US ), BS (UK), EN/EN04 (EU , UNI (IT) GB-Civil/GB/GB10 (C N), JIS(Civil)/JIS (JP), KS(MKS )/KS(SI) (KR)

The user may check the corresponding material standard’s rebar names, diameters, maximum diameters, section area, unit weight, and strength by clicking on the […] button.

Figure 3.2.1 Rebar Material set up dialog window

Section 2. Rebar/Arrangement | 91

DESIGN REFERENCE


Figure 3.2.2 Dialog window for checking the rebar material standard list

The u ser m ay specify the rebar material strength by using either Batch Se tting or Individual Setting.

►

Batch Setting : Rebars are divided into main and shear reinforcements. The same strengths

are app lied regardless o f the diameter. ►

Individual Setting : Different strengths are applied depending on the rebar diameter. The user

may specify the member type (beam, column, brace, plate) and main/shear reinforcement by clicking on the […] button and then specify the strength depending on the diameter.

Figure 3.2.3 Dialog window for setting rebar material strengths

92 | Section 2. Rebar/Arrangement

DESIGN REFERENCE



DESIGN REFERENCE


Setting Rebar Default Values ►

Cover thickness

Cover thickness decides the starting location for the rebar. The cover thickness may be defined following one of the two processes below. - Clear Cover: The thickness extends from the concrete edge to the outermost rebar surface - Con’c Edge~ Rebar Center: The thickness extends from the concrete edge to the rebar center

Figure 3.2.4 Cover thickness set up procedure

Whe n calculating the strength of an RC m ember, steel location is an important parameter. If “Clear Cover” is selected, the first rebar center’s location is calculated using the cover thickness, the shear rebar diameter, and half of the m ain rebar diameter.

d c = Clear Cover + Dia shear + 0.5Diamain


(3.2.1)


DESIGN REFERENCE

► Basic information regarding rebar calculations for each member type

This section explains the setting of default values for important rebar parameters su ch as ce nter cover thickness, main reinforcement diame ter, largest steel ratio, ma in reinforcement coupling method, shea r reinforcemen t diameter, etc.

The concrete cover thickness and the steel diameter’s default values are considered when first creating the rebar arrangement, and the m ain reinforcement coupling method is used w hen ca lculating the possible number of rebars. For example, the calculation for possible number of rebars for a single layer due to clear cover limits is shown below.

Table 3.2.1 Calculation method for possible number of rebars depending on the

(Beam depth 2X center cover thickness + clear cover rule + –

Neglected

main reinforcement diameter)

N=

Steel clear cover rule (Beam depth 2X center cover thickness + clear cover rule + –

50%

main reinforcement diameter)

N=

0.5X main reinforcement diameter + clear cover rule (Beam depth 2X center cover thickness + clear cover rule + –

100%

N=

main reinforcement diameter) 1.0X main reinforcement diameter + clear cover rule

► Defining the reinforcement based on the member type

This section explains the process for defining the steel’s maximum/minimum diameters and maximum/minimum spacing depending on the member type and section measurements. For bea ms, the section height is used as the basis to determine the ma in reinforcemen t which will then govern the ma ximum/minimum d iameter for the m ain reinforcement and the greatest number of rebars. The shear steel reinforcement will determine the maximum/minimum diameter, maximum/minimum spacing, and the spacing increment. The outer steel determines the minimum/maximum diameter. The Section 2. Rebar/Arrangement | 95

DESIGN REFERENCE


main steel starts with the minimum diameter, whereas the shear steel starts at the minimum diameter and minimum sp acing. Then, the program analyzes the required amount of steel for the expected demand and finds the rebar arrangement that best satisfies spacing requirements and steel ratio requirements.

Figure 3.2.5 Shear rebar design settings dialog window



DESIGN REFERENCE

For columns and braces, the section measurements’ minimum values are used as the basis and the main reinforcement decides the minimum and maximum diameters. The shear reinforcement determines the maximum/minimum diameter, maximum/minimum spacing, and spacing increment. The main reinforcement begins at the minimum diameter, and the shear reinforcement begins at the minimum diam eter and minimum spacing. The program then ana lyzes the required amou nt of steel for the expected demand and finds the steel rebar arrangement that best satisfies the spacing and steel ratio requirements.

Figure 3.2.6 Column rebar design settings dialog window

For plate members, the minimum plate thickness is used as the basis. The main reinforcement dictates the maximum/minimum diameter, upper/lower reinforcement numbers, maximum/minimum spacing, and the spacing increment. The shear reinforcement dictates the maximum/minimum diameter, maximum/m inimum spacing, and the spacing increment.

Figure 3.2.7 Plate rebar design settings dialog window

The shear reinforcement makes a list of combinations of the diameter and leg number, and proceeds with the rebar creation in a sequential manner. The diameter list is defined from the m inimum diameter to the maximum diameter, and the leg list is defined from two to the maximum number of legs. The maximum numb er of legs is decided by taking into account the num ber of shear reinforcement rebars and the clear cover restrictions, and chooses the maximum possible number of legs. The number of legs that takes into account the steel clear cover restriction is calculated as follows.


DESIGN REFERENCE


Leg space =

B - 2d c , side

smax, trans + d shearbar

Here, d c, side

: Side cover thickness from the concrete edge to the center of steel rebar

smax,trans

: Maximu m stee l spacing for the lateral direction (industry standard value)

d shearbar

: Diameter of shear rebar


(3.2.2)


DESIGN REFERENCE

For example, when the shear reinforcement steel diameter range is between D10-D16 and the maximum numb er of legs is 4, the following list is created and com puted in sequential order for shear reinforcemen t calculations.

Table 3.2.2 Sample list of the

D10

D13

D16

shear reinforcement cre ation list when the maximum

2 Leg

① D10 X 2 leg

② D13 X 2 leg

③ D16 X 2 leg

numb er of legs is 4

3 Leg

④ D10 X 3 leg

⑤ D13 X 3 leg

⑥ D16 X 3 leg

4 Leg

⑦ D10 X 4 leg

⑧ D13 X 4 leg

⑨ D16 X 4 leg


DESIGN REFERENCE

S e ctio n 3


Co m m on D esign Co nsiderations Mome nt Redistribution Factor [Applicable Membe r: Beams] Typically, for statically indeterminate RC structures, a single section failure does not bring structural collapse and there is a significant difference in dem and required to b ring about the first failure and total collapse. Therefore, simply because an indeterminate beam has reached its ultimate mom ent does not mean immediate failure. Before reaching the state of failure, the load will increase and create a plastic hinge. This w ill then a ffect the mom ent distribution, and the phe nome non is called the redistribution of moment. That is to say, the state at which failure occurs, the section has plastic resistance. In parts of the member where rotation is allowed, or where the plastic hinge has formed, moment does not change. The moment will instead increase where there is low strength, and this is called moment redistribution. The mo ment redistribution factor aims to reflect such pheno mena in R C beam s, and the design forces that incorporates the m omen t redistribution are is calculated as follows.

Figure 3.3.1 Design force calculation Case 1 when incorporating the mo ment redistribution factor

100 | Section 3. Common Design Considerations


DESIGN REFERENCE

[ Case 01 ]

Mi Mj Mi’

x M

Mj ’

’ x

M

X L

Put β = Redistribution Factor Modified M oment At I-end : M i’= |Mi| (1-β) Modified M oment At J-end : Mj’= |Mj|(1-β) Modified Moment at location X : Mx ’= Mi’+ X/L *(Mj ’-Mi’) Redistribution Moment at location X : Mxre = Mx + Mx ’ •

•

•

•

[ Case 02 ]

Mj

Figure 3.3.2 Case 2 for

Mj

calculating the design forces

’

while incorporating the mom ent redistribution factor Mi Mi

’

Put β = Redistribution Factor Check Mi = (+) Positive, Mj = (-) Negative . Modified Moment At I-end : Mi = |Mj| (1-β) •

’

Modified Moment At J-end : Mj = |Mj| (1-β) Modified Moment at location X : Mx = Mi + X/L *(Mj -Mi ) Redistribution Moment at location X : Mxre = Mx + Mx

•

’

•

’

’

’

’

•

’

The mo ment redistribution factors may be set for either the entire model or for individual members. Factors set for individual mem bers w ill override the m odel-wide values if both have been defined.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Section 3. Common Design Considerations | 101

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Figure 3.3.3 Dialog window showing how to set the mom ent redistribution factor for the entire mod el

Analysis & Design>Analysis & Design>Mem ber Parameters>Mo ment Redistribution Factor Figure 3.3.4 Dialog window showing how to set the mom ent redistribution factor for a specific mem ber

102 | Section 3. Common Design Considerations


DESIGN REFERENCE

S e ctio n 4

Design Considerations- ACI318-11 Strength Reduction Factor Tension-controlled section strength reduction factors, compression-controlled section (hooped reinforcement, etc) strength reduction factors, and shear strength reduction factors can be set. The default values are the industry standard, but the user may specify alternative values. A single set of strength reduction factors is applied to the entire model.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.4.1 Dialog window for setting the strength reduction factors

Mome nt Magnifiers δns, δs [Applicable mem bers: columns, braces] Moment magnifiers are used to approximate second order analysis results using first order analysis results, to incorporate second order effects without conducting a full analysis. Mome nt magn ifiers are automatically computed for laterally braced and unbraced members. If the member’s effective length factor k is less than 1.0, then the mem ber is considered to be laterally braced. δ ns is a mome nt magnifier that aims to incorporate P-δ effects that occur due to strains developing in the structure, and is supported by automa tic computation in this program. It is calculated as follows:

d ns =

1-

C m P u

(3.4.1)

0.75 P c

Here,

Section 4. Design Considerations - ACI318-11 | 103

DESIGN REFERENCE


C m = 0.6 + 0.4

P c =

EI =

M 1 M 2

p 2 EI

( kl u )2 0.2 E c I g + E s I se 1 + b ns

δ s is a moment mag nifier that aims to incorporate P-Δ effects that occur due to local displaceme nts, and is calculated as follows:

d s =

1

å P 10.75å P

³1

(3.4.2)

u

c

Howe ver, δs is not automatically compu ted in this program. Unless the user specifies a value, 1.0is applied as the de fault value.

Moment magnifiers may be set to be automatically determined for the entire model, and individual members may be set to take on the automatically computed values or alternative, user-specified values. The p rogram o verrides the a utomatically determined values with any user-specified va lues for memb ers that have such alternate values defined.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.4.2 Dialog window for setting automatic computation of mo ment magnifiers

Analysis & Design>Analysis & Design>Member Parameters>Moment Magnifier Factor

104 | Section 4. Design Considerations - ACI318-11


DESIGN REFERENCE

Figure 3.4.3 Dialog window for setting the mom ent magnifier factors for individual members

Seismic Design Shear Calculations [Applicable membe rs: beam, column] Whe n considering seismic design of structures, the design mu st account for additional shear forces for seismic considerations. The program uses the following methods to calculate the seismic design shear.

Table 3.4.1 Seismic Design

Calculation

Shear calculation methods

Method

Shear Calculation

Max (V e 1 , V e2 )

The maximum of the two values V e 1 , V e 2 (which incorporate the additional shear factors a 1 , a 2 )

Min (V e 1 , V e 2 )

The minimum of the two values V e 1 , V e 2 (which incorporate the additional shear factors a 1 , a 2 ) is used. However, if the seismic design shea r is smaller than th e analyzed shear forces, then the analyzed shear forces are used instead. Shear is added by using the weak shear-strong bending principle. Shear strength is calculated by applying the additional shear factors a1 . a 1 is specified by the user, and can use the industry standard as the default value. If the earthquake resisting system is SMF, M pr V e1 = V g + a1 l M pr : calculated expected bending strength assuming tensile yield strength of 1.25f y and streng th reduction factor of 1.0 If the earthquake resisting system is IMF,

å

V e1

V e1 = V g + a1

å M

n

l

Section 4. Design Considerations - ACI318-11 | 105

DESIGN REFERENCE


V e2

The shear force due to earthquake loading is increased. Shear strength is calculated by using the additional shear factor a2. a2 is specified by the user, and can use the industry standard as the default value.

V e2 = V g + a2V eq

Seismic design criteria are applied to the entire model.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.4.4 Dialog window setting se ismic design criteria to the entire model

106 | Section 4. Design Considerations - ACI318-11


DESIGN REFERENCE

S e ctio n 5

M em ber Examination Procedure (Beams)-ACI318-11 The me mber verification procedure for RC beam s following the ACI318-11 design code is explained in this section. The design strength is calculated using the analyzed strengths, load combinations, and design strength modificatio n factors. Industry standard strengths are compu ted to verify the mom ent, shear, and m ain reinforcement spac ing, to ensure con sistency. For serviceability, immediate deflections, long term deflections, and o uter rebar spacing are checked.

Calculation of Design Demand s The design strengths are calculated by applying load combinations, live load reduction factors, mome nt redistribution factors, and seismic design criteria to the analyzed strengths.

Section 5. Member Examination Procedure (Beams) - ACI318-11 | 107

DESIGN REFERENCE

108 | Section 5. Member Examination Procedure (Beams) - ACI318-11



DESIGN REFERENCE

1) Application of load combinations

The design forces are calculated, factoring in the member check points, load types, and load combination factors. 2) Application of live load reduction factors

As explained in the section Design Factors>Live Load R eduction factors, components that are subject to live loads will have design forces that incorporate the live load reduction factor. 3) Application of Moment Redistribution Factors

Between both ends of a beam in which minor axis mome nts are present, at least one end is selected for application of a mom ent redistribution factor less than 1.0 (as explained in D esign Factors>M omen t Redistribution Factors). Then, the design moment incorporating the moment redistribution factor is calculated. 4) Application of Seismic Desi gn Criteria

When seismic design criteria are used, the design shear and moment are calculated differently, depending on the earthquake resisting system.

Table 3.5.1 Design shear and

SMF

IMF

mom ent calculations depending on the earthquake resisting s ystem

Shear


DESIGN REFERENCE


Moment

As for design shear, one of the two methods is applied—either the strong shear-weak bending principle method or additional shear method—depending on the user’s preference. If the earthquake resisting system is a special moment frame, then the design shear as per the strong shear-weak bending principle may be calculated as shown below.

Table 3.5.2 Design shear calculations for a special mom ent frame, using the strong shear-weak bending

V e1,cw,1 = V g + a1

M pr ,i ( + ) + M pr , j ( -)

V e1,cw, 2 = V g - a1

l n M pr ,i( + ) + M pr , j ( - ) l n

[

V e1,cw = max V e1,cw,1 , V e1,cw,2

]

V e1,ccw,1 = V g + a1

M pr ,i (- ) + M pr , j ( + )

V e1,ccw, 2 = V g - a1

[

l n M pr ,i ( -) + M pr , j ( + ) l n

V e1,ccw = max V e1,ccw,1 , V e1,ccw,2

]

V e1 = max[V e1,cw , V e1,ccw ]

The de sign shear incorporating add itio nal shear due to e arthquake loads can be calculated as shown below. V e2 = V g + a2V eq

(3.5.1)

Calculation of Design Strengths The design strength of each memb er is based on load combinations and must be greater than the calculated required strength. Ru £ f Rn

Ru

: Requ ired strength

Rn

: Nominal strength


(3.5.2)


DESIGN REFERENCE

Φ

: S tre ngth re du ctio n fa cto r

1) Flexural/Bending strength

Major and minor bending strengths must be greater than the moment demands expected in the structure. The main re inforcement ratio should satisfy the m aximum/minimum steel ratio limits. M u (+ ) £ f M n( +)

(3.5.3)

M u( -) £ f M n( -)

(3.5.4)

r min £ r £ r max

(3.5.5)


DESIGN REFERENCE


Neutral axis location is the most important number in calculating the flexural strength. Iterative methods are used to find the solution that satisfies force equilibrium.

Using c as the neutral axis, the compressive force taken on by the concrete C c is as follows:

C c = 0.85 f c ab

Here, a = b 1c

( f c £ 4000 psi ) 0.85 ì ï f b 1 = í é ù max ê1.05 - 0.05 c , 0.65ú ( f c > 4000 psi ) ïî 1000 ë û


(3.5.6)


DESIGN REFERENCE

Figure 3.5.1 Neutral axis location for a high strength RC block

C sis the force taken on by the com pressive steel and T s is the force taken on by the tensile steel:

å A ( f - 0.85 f ) T = å A f C s =

s

sci

sti

si

(3.5.7)

c

si

(3.5.8)

Here ,

[

f si = min f y , e si E si

]

ì d i - c ( c < d i ) ïe cu c e si = í c - d i ïe cu ( c ³ d i ) c î

This program uses the bisection method (one of the numerical analysis methods) to find the neutral axis. The principal equation of the bisection method is C c + C s = T s . Convergence/stopping criteria are shown below.

Table 3.5.3 Neutral axis

Stopping Criteria

calculation methods and corresponding stopping

Convergence

Description C c + C s T s

- 1.0 £ 0 .001 ( tolerance )


DESIGN REFERENCE


No convergence

When the number of iterations is larger than 20 , it is deemed that

(Stop

convergence will not be reached. The section is either increased or the rebar

computations)

information is m odified (location, num ber of rebars, spacing, etc).



DESIGN REFERENCE

After locating the neutral axis, the nominal flexural strength is calculated as sho wn be low. M ncc = C c ( c - 0.5a ) = C c ( c - 0.5b 1c)

(3.5.9)

M nsc = C si ( c - d i )

(3.5.10)

M nst = T si ( d i - c )

(3.5.11)

M n = M ncc + M nsc + M nst

(3.5.12)

The design lateral strength is the product of the nominal strength and the strength reduction factor (whose calculations are shown be low and depends on the outermost tensile steel strain ε t).

Figure 3.5.2 Strength Reduction Factors

The minimum and ma ximum steel ratios of the main reinforcement is shown be low.

é

Table 3.5.4 Minimum and

r min1 = maxê3.0

maximu m steel ratios for the main reinforcement

êë

r min

r min 2 =

4 3

f c f y

,

200ù

ú

f y úû

r req

r min = min [ r min 1 , r min 2 ]


DESIGN REFERENCE


r max = r b = 0.85b 1

r max

f c

e cu

f y e cu + 0.004

If the earthquake resisting system is SMF and if earthquake design criteria are to be applied, r max = min[ r b , 0.025]



DESIGN REFERENCE

2) Shear Strength The design shear strength must be greater than the expected shear demands. The shear reinforcemen t spacing must be less than the ma ximum sp acing set by the industry standards. V u £ f V n s £ smax

(3.5.13) (3.5.14)

The design shear strength is the product of the strength reduction factor, and the sum of the shear forces taken on by the concrete and sh ear reinforcement.

f V n = f (V c + V s )

(3.5.15)

The she ar force taken on by the concrete is determined as follows:

V c = 2 f c bd

(3.5.16)

Howe ver, if the earthquake resisting system is SMF and ea rthquake design criteria are to be applied, then the user-specified shear co ntribution of concrete will be m ultiplied to the above value. The shear contribution of concrete m ay be set in Design Settings>General>Design Code>Seismic Design>Shear for Design in Seismic Deisgn .

Figure 3.5.3 Dialog window showing the setup of shear contribution of concrete in

The sh ear force taken on b y the shear reinforcement is calculated a s follows: Section 5. Member Examination Procedure (Beams) - ACI318-11 | 117

DESIGN REFERENCE


V s =

nA sv1 f yt d s

Here, n : Number of legs of the shear reinforcement


(3.5.17)


DESIGN REFERENCE

The required shear reinforcemen t steel amount depends on th e shear force, as shown below . Figure 3.5.4 The required amou nt of steel depending on the shear force

The ma ximum spa cing limits are depende nt on the seismic design criteria and whether they are be ing applied.

Table 3.5.5 Maximum spacing limits bas ed on application of seismic design criteria

No seismic design criteria

é d ù s max, 0 = minê , 24 in ú ë2 û

▶SMF

Seismic design criteria applied

é d ù s max, 0 = minê , 6in, 6 Dmain ú ë4 û

▶IMF é d ù s max, 0 = min ê , 12 in, 8 Dmain , 24 Dstirrup ú ë2 û

The ma ximum spacing limits depending on the shear force is shown below.

Figure 3.5.5 Maximum spacing limits as a function of shear force


DESIGN REFERENCE

Se ction 6


Member

Examination

Procedure (Columns/Braces) ACI318-11 The memb er examination procedure for RC columns/braces as per the ACI318-11 design code is explained in this section. The design strength is calculated using the analyzed strengths, load combinations, and design strength modification factors. Industry standard strengths are compu ted to verify the axial forces, mome nts, and shear forces.

120 | Section 6. Member Examination Procedure (Columns/Braces) - ACI318-11


DESIGN REFERENCE

Calculation of Design Demand s Design demands/forces are computed by applying load combinations, live load reduction factors, mome nt ma gnifiers, and sp ecial seismic design criteria.

1) Apply Load Combinations The ana lyzed demand s at the membe r check points, load types, and the load comb ination factors are incorporated in compu ting the design dema nds.

2) Applying the live load reduction factor As explained in the section Design Fa ctors>Live Load Reduction Fa ctors, compo nents that are subject to live loads will have design forces that incorporate the live load reduction factor.

3) Applying the moment magnifier Whe n designing column s/braces, sections are designed d ifferently depending on the slenderness ratio. If the me mber is a long column, then mom ent magnifiers are used in calculating the design lateral moment. The second order moment—incorporating the analytical first order moment and moment magnifiers— are calculated depending on the lateral bracing conditions, as shown below. This program decides the bracing conditions based on the mem ber’s effective buckling length factor.

T a bl e 3 .6 .1 2 n d order

Braced

K ≤ 1.0

mom ents depending on the lateral bracing conditions

Unbraced

K > 1.0

M c = d ns M 2 M 1 = M 1ns + d s M 1 s M 2 = M 2ns + d s M 2 s

Here, M2

= The larger of the end lateral mome nts of the com pressive member

Section 6. Member Examination Procedure (Columns/Braces) - ACI318-11 | 121

DESIGN REFERENCE


M 1n s

= The end lateral moment calculated using 1 st order elastic frame analysis and loads that do not cause lateral strains at the end at which M 1 is applied . This program uses mom ents due to dead an d live loads.

M 1s

= The end lateral moment of the compressive mem ber, calculated using 1 st order elastic frame analysis and loads that cause lateral strains at the end at which M 1 is applied. This program uses m oments due to all loads except for dead an d live loads .

M 2n s

= The end lateral mom ent of the compressive mem ber, calculated using 1 st order elastic frame analysis and loads that do not cause lateral strains at the end at which M 2 is applied. This program uses mom ents due to dead and live loads .

M 2s

= The end lateral moment of the compressive mem ber, calculated using 1 st order elastic frame analysis and loads that cause lateral strains at the end at which M 2 is applied. This program uses m oments due to all loads except for dead an d live loads .

However, load combinations that include P-Δ analysis criteria (which are part of second order analysis) do not use mom ent mag nifiers.



DESIGN REFERENCE

4) Ap plying special seismic design criteria The design shear forces must be calculated differently depending on the resisting system, if seismic design criteria are being applied.

Table 3.6.2 Design shear

SMF

IMF

force calculations for different earthquake resisting systems

Shear

Design shear forces may be calculated using either the strong shear-weak bending principle method or the add itional shear m ethod. The user may specify his or her preference within the program settings. If the earthquake resisting system is a special mom ent frame, then the design shear is calculated using the strong shear-weak bending principle.

Table 3.6.3 Design shear calculations for spe cial mom ent frames, using strong shear-weak bending

V e1,cw,1 = V g + a1

M pr ,i ( + ) + M pr , j ( -)

V e1,cw, 2 = V g - a1

[

l n M pr ,i( + ) + M pr , j ( - ) l n


]

V e1,ccw,1 = V g + a1

M pr ,i (- ) + M pr , j ( + )

V e1,ccw, 2 = V g - a1

[

l n M pr ,i ( -) + M pr , j ( + ) l n


]


The de sign shear force with the additional shear due to earthquake loading is calculated as follows. V e2 = V g + a2V eq

(3.6.1)


DESIGN REFERENCE


Calculation of d esign strengths The design strength of each memb er is based on load combinations and must be greater than the calculated required strength. Ru £ f Rn

(3.6.2)

Here, R u : Required strength R n : Nominal strength Φ : Strength reduction factor 1) Axial-lateral strength

To calculate the design strengths of members subject to both axial and lateral loading, the correlation between axial-lateral forces mu st be incorporated. In this program, the P-M correlations are incorporated into the computation of axial and lateral strengths. The main reinforcement ratio must satisfy the minimum and maximum steel ratio limits. P u £ f P n

(3.6.3)

M u £ f M n

(3.6.4)

M uy £ f M ny

(3.6.5)

M uz £ f M nz r min £ r £ r max

(3.6.6) (3.6.7)

Com pressive me mbers sub ject to pure axial force (without eccentricity) have design a xial strengths that are calculated as show n below. Table 3.6.4 Design axial

Spiral

strengths of compressive

reinforcement

members, depending on reinforcem ent type

Hoop reinforcement

f P n ,max = 0.85f [0.85f c ( Ag - Ast ) + f y Ast ] f P n ,max = 0.80f [0.85f c ( Ag - Ast ) + f y Ast ]


DESIGN REFERENCE


Column/brace memb ers sub ject to bo th axial and lateral loads must satisfy force equilibrium and strain compa tibility criteria. Stress-strain relationships for biaxial P-M correlations are sho wn b elow.


DESIGN REFERENCE



Figure 3.6.1 Stress-strain relationship for Biaxial P-M correlation


DESIGN REFERENCE

The axial force and lateral force is calculated using eccentricity. Using the resulting values, the P-M correlation curve is calculated. Throug h the correlation curve, the design sh ear corresponding to the desired force may be found.


DESIGN REFERENCE

Figure 3.6.2 Uniaxial P-M correlation (nominal strength)

그림 3.6.3 Uniaxial P-M correlation (design strength)



DESIGN REFERENCE


Figure 3.6.4 B iaxial P-M correlation

Figure 3.6.5 P-M correlation for a specific load combination

The minimum and ma ximum steel ratios for the main reinforcement are shown be low.


DESIGN REFERENCE


Table 3.6.5 Minimum and maximu m steel ratios for the

r min

0.01

main reinforcement

r max

User-specified

2) She ar strength The design shear strength must be greater than the expected design shear demands. The main reinforcemen t spacing must b e smaller than the m aximum spacing limits set by industry standards. V uy £ f V ny

(3.6.8)

V uz £ f V nz s £ s max

(3.6.9) (3.6.10)

The design shear strength is the product of the strength reduction factor and the sum of the shear force taken on by the concrete and sh ear reinforcemen t. f V n = f (V c + V s )

(3.6.11)

The shear force taken on by the concrete is a function of the axial force, as show n below.

Table 3.6.6 Shear forces taken on by the co ncrete, as

P=0

a function of the axial force

V c = 2 f c bd

æ ç è

Tensile force

V c = 2ç1 +

Compressive force

V c = 2ç1 +

æ ç è

ö ÷ f c bd 2000 A g ø÷ N u

N u ö

÷ f c bd

500 A g ø÷

Howe ver, if the earthquake resisting system is SMF an d seismic design criteria are to be app lied, then the user-specified concrete shear contribution actors are to be multiplied.



DESIGN REFERENCE

The she ar strength taken on b y the shear reinforcemen t steel is calculated as shown be low. V s =

nA sv1 f yt d s

(3.6.12)

Here, n : numb er of legs of the main reinforcement

The required shear reinforcement amo unts are dependent on the shear force, as shown below:

Figure 3.6.6 Required shear steel reinforcement amounts as a function of shear force

Maximum spacing limits for shear reinforcement are calculated differently depending on the application of seismic design criteria, rebar arrangement (end/interior portions), type of shear reinforcemen t (hoop/spiral). The m aximum spacing limits for rectangular sections are shown below.

Table 3.6.7 Maximum spacing

No seismic design

limits for rectangular sections

criteria

smax,0 = min[16Dmain , 48 D shear , H , B]

as a function of seismic ▶

design criteria

SMF é d ù s max, 01 = minê , 6in, 6 Dmain ú ë4 û é14 - h x ù s max,02 = 4 + maxê ,0ú ë 3 û A sh

s max, 03 =

Application of seismic

0.3hc

design criteria (Ends) smax, 04 =

f c æ A g

ö çç - 1÷÷ f ys è Ac ø

A sh 0.09hc

f c f ys

smax,0 = min[ smax,01, smax,02 , smax,03 , smax,04 ]

▶ IM F


DESIGN REFERENCE


é H B ù s max, 0 = minê , , 8 Dmain , 24Dstirrup , 12 in ú ë2 2 û ▶

SMF


Application of seismic

smax,02 = min[ 6Dmain , 6in]

design criteria

smax,0 = min[ smax,01 , smax,02 ]

(Interior) ▶ IM F smax,0 = min[16Dmain , 48 D shear , H , B]



DESIGN REFERENCE

Maximum spacing limits for circular circular sections are as follows. follows.

Tablee 3.6 Tabl 3.6.8 .8 Maxi Maximum mum spaci spacing ng

No seismic design

limits for circular sections as a

criteria


function functi on of seism ic design ▶

SMF (Hoop Reinforcement Reinforcement)) é d ù s max, 01 = min ê , 6in, 6 Dmain ú ë4 û s max, 03

2 p D shear smax,02 = f 0.12 H c f ys

é14 - h x ù ,0ú = 4 + maxê ë 3 û

smax,0 = min[ smax,01, smax,02 , smax,03 ]

Application of seismic design criteria (End)

▶ SMF (Spiral (Spiral Reinfo Reinforc rcement ement)) é

ö f f ù - 1÷÷ c , 0.12 c ú f ys ûú è Ac ø f ys æ A g

r s = max ê0.45çç

ëê

s max, 0

2 é ù é p D shear ù , D shear + 1in ú, Dshear + 3in ú = minê max ê ë r s d c û ëê ûú

▶ IM F é H ù s max, 0 = min ê , 8 Dmain , 24 Dstirrup , 12 in ú ë2 û ▶

SMF r s = 0.12

Application of seismic design criteria

s max, 0

f c f ys

2 é ù é p D shear ù , D shear + 1in ú, Dshear + 3in ú = minê max ê ë r s d c û ëê ûú

(Interior) ▶ IM F smax,0 = min min[16Dmain , 48 D shear , H , B]

Section Sect ion 6. Member Examina Examination tion Procedure Procedure (Columns/Braces) - ACI318-11 | 13 133 3

DESIGN REFERENCE


Maximum spacing limits are a function function of the shear force, as shown below.

Figure Fig ure 3.6 3.6.7 .7 Maxi Maximum mum spacing limits as a function of shear force

134 | Sec Section tion 6. Mem Membe berr Examinat Examination ion Proce Procedure dure (Columns/Braces) - ACI318-11


DESIGN REFERENCE

Se ction ction 7

Design ign Par Paramet meters EN19921-1:2004 Partial Factors This secti section on explains explains how to set parti partial al factors factors (γ c,Fundamental , γ c,Accidental ) for long-t long-term erm and short-term short-term loading on concrete and partial partial factors factors (γ s,Fundamental, γ s,Accidental ) for long-term long-term and short-term short-term loading on steel, as well as the the long-term loading effective effective factor (α cc ). Industry standards are programmed as default values, but the user m ay m odify these values. Partial factors factors are ap plied to the entire model.

Home>D esign Settings Settings>General >General>Design >Design Code>RC >Code-Specifi >Code-Specificc RC Design Parameters Figuree 3.7. Figur 3.7.11 Dialo Dialogg window for setting the partial factor for the entire model

Slenderness Limitation Limitation [Applicable [Applicable Membe rs: Columns, Braces] If the the mem ber’s slendernes slendernesss ratio ratio λ is smaller smaller than the slenderness slenderness limi limitat tation ion λ lim , then the member’s second o rder effects may be ignored. The slenderness limitation limitation is calculated calculated as sh own b elow.

l lim =

20 2 0 × A × B × C n

(3.7.1)

Here, A =

1 1 + 0.2f ef

: this is specified by the user in this program.

Section Sect ion 7. Design Param Parameters eters EN1992-1-1:2004 | 13 135 5

DESIGN REFERENCE


B =

1 + 2w

:

this is specified by the user in this program

.

C = 1 .7 - r m

f ef = effect effectiv ivee creep creep rati ratio. w =

n =

A s f yd Ac f cd

N Ed Ac f cd

r m =

M 01 M 02

M 01 , M 02

= 1 st order order end moment momentss ( M 02 ³ M 01 )

To calculate the slenderness limitati limitation, on, parameters A, B, C are input and used for the entire model. Home>D esign Settings Settings>General >General>Design >Design Code>RC >Code-Specifi >Code-Specificc RC Design Parameters Figuree 3.7. Figur 3.7.22 Dialo Dialogg window for setting setting the slenderness lilimitation mitation for the entire mo del

Seismic Design Criteria Criteria In this program, the basic value of the behavior factor q o is used to calculate the curvature ductility factor, and isis calculated as shown below. Th e user may s pecify α u/α 1 and q o directly. Table 3.7.1 Behavior factor factor q0 as a function function of the system type

S y s t e m ty p e

D CM

D CH

Frame system, Dual system, Coupled w all system system

3.0α u / α 1

4.5α u / α 1

Uncoupled w all system system

3 .0

4 .0 α u/ α 1

Torsionally flexible system

2 .0

3 .0

Inverted Inverted pendulum system

1 .5

2 .0

The curvature ductility ductility factor μ φ is calculated as follows: m f = 2q0 - 1 (T 1 ³ T C ) 136 13 6 | Se Secti ction on 7. Des Desig ign n Par Param amet eter ers s EN1992-1-1:2004

(3.7.2)


DESIGN REFERENCE

m f = 1 + 2( q0 - 1)

T C T 1

(T 1 < T C )

(3.7.3)

γ Rd , which is used to calculate the end mom ent M i,d for seismic design she ar, takes on different values for beams and columns, as shown below. Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.7.3 Dialog window for setting the curvature ductility factor for the entire

Section 7. Design Parameters EN1992-1-1:2004 | 137

DESIGN REFERENCE

Se ction 8


Member

Examination

Procedure (Beams) -EN1992-1-1:2004 The member examination procedure for RC beams as per the EN1992-1-1:2004 design code is explained in this section. The design forces are calculated by applying load combinations and design modification factors. Major/minor mo ment an d shear forces are checked using industry standard values. Fo r serviceability, cracks, stress, and deflections are checked.

138 | Section 8. Member Examination Procedure (Beams) - EN1992-1-1:2004

DESIGN REFERENCE


Section 8. Member Examination Procedure (Beams) - EN1992-1-1:2004 | 139

DESIGN REFERENCE


Calculation of Design Dem ands/Forces Design demands/forces are computed by applying load combinations, live load reduction factors, mome nt redistribution factors, and seismic design criteria.

1) Applying load combinations The analyzed deman ds at the mem ber check points, load types, and the load combination factors are incorporated in compu ting the design dema nds.

2) App lying the live load redu ction factor The ana lyzed demand s at the membe r check points, load types, and the load comb ination factors are incorporated in compu ting the design dema nds. 3) Applying moment redistribution factors

Between both ends of a beam in which minor axis moments are present, at least one end is selected for application of a mom ent redistribution factor less than 1.0 (as explained in D esign Factors>M omen t Redistribution Factors). Then, the design moment incorporating the moment redistribution factor is calculated. 4) Ap plying special seismic design criteria If seismic design criteria are to be applied, then the strong shear-weak bending is applied to load combinations including earthquake loads an d the design shear forces are calculated as sho wn below.

Table 3.8.1 Calculation of design shear forces using the strong shear-weak bending principle, when applying seismic d esign criteria

V e1,cw,1 = V g +

M i,d ,i ( + ) + M i ,d , j ( - )

V e1,cw, 2 = V g -

[

V e1,ccw,1 = V g +

l n M i ,d ,i ( + ) + M i ,d , j ( - )

V e1,ccw, 2 = V g -

l n


]

[

M i ,d ,i ( - ) + M i,d , j ( + ) l n M i ,d ,i ( -) + M i ,d , j ( + ) l n


]


End moments M i,d are used in com puting design shear, and are calculated as follows: 140 | Section 8. Member Examination Procedure (Beams) - EN1992-1-1:2004


DESIGN REFERENCE

é

M i,d = g Rd M Rb,i min ê1,

ëê

å M å M

ù ú ú Rb û

(3.8.1)

Rc

Here, γ Rd

= Fa ctor incorporating the increased strength due to strain hardening of steel. Specified by the user

M Rb,i

= Design moment for the end of the member

Σ M Rc

= Sum o f the design mome nts of column node s

Σ M Rb

= Sum of the design moments of beam nodes Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters

Figure 3.8.1 Dialog window for setting d esign shear force parameters for the entire

ULS: U ltimate L imit State The design strength of each structural member mu st exceed the required strength comp uted from the load combinations.

1) Bending/Flexural S trength

Design flexural strength (based on the major/minor moments) must exceed the required flexural strength. The main reinforcemen t must satisfy the minimum and m aximum stee l ratios. M Ed ( + ) £ M Rd ( + ) M Rd ( -) £ M Rd ( -)

(3.8.2)

(3.8.3)


DESIGN REFERENCE


r min £ r £ r max

(3.8.4)

The location of the neutral axis is the most important number in com puting the flexural strength of a memb er. Iterative m ethods are u sed to find the solution that satisfies equilibrium.

If x is the neutral axis, then the compressive force taken on by the concrete, C c, is calculated as:

C c = h f cd

ò

dA

l x

Here, λ : effective height factor of the compressive portion of the concrete η : effective strength factor


(3.8.5)


DESIGN REFERENCE

Table 3.8.2 Effective height

Criteria

λ

η

f ck ≤ 50MPa

0.8

1.0

50 < f ck ≤ 90MPa

0.8-(f ck -50)/400

1.0-(f ck -50)/200

f ck > 90MPa

0.7

0.8

and strength factors depending on the compressive force in the concrete

x : De pth of the neutral axis

Figure 3.8.2 Height of the neutral axis for a high strength RC block

The compressive force taken on by the steel, C s , and the tensile force taken on by the steel, T s, is calculated as follows.

å A ( f - hf ) T = å A f

C s =

sci

s

si

sti

cd

si

(3.8.6) (3.8.7)

Here,

[

f si = min f yd , e si E si e si =

d i - x x

]

e cu


DESIGN REFERENCE


Figure 3.8.3 Strain distribution at the ultimate limit state

ε cu : ultimate com pressive strain of concrete (ε cu = ε cu 1 ) 표 3.8.3 Ultimate compressive strain depending on the compressive strength of concrete

Criteria

ε cu 1

fck ≤ 50MPa

0.0035

50 < fck ≤ 90MPa

[2.8+27{(98-f cm )/100}4]/1000, f cm = f ck +8MPa

fck > 90MPa

0.0028

This program uses the bisection method (one of the numerical analysis methods) to find the neutral axis. Convergence /stopping criteria are sho wn below.

Table 3.8.4

Stopping Criteria

Converge nce/stopping criteria for locating the neutral axis

Convergence

Description C c + C s T s

- 1.0 £ 0 .001 ( tolerance )

No convergence

When the number of iterations is larger than 20 , it is deemed that

(Pause

convergence will not be reached. The section is either increased or the rebar

computations)

information is m odified (location, num ber of rebars, spacing, etc).

After locating the neutral axis, the design bending strength is com puted as follows.



DESIGN REFERENCE

(3.8.8)

M Rdcc = C c ( x - 0 .5 l x )

å C ( x - d ) = åT ( d - x)

M Rdsc = M Rdst

si

si

(3.8.9)

i

(3.8.10)

i

M Rd = M Rdcc + M Rdsc + M Rdst

(3.8.11)

The minimum /maximum steel ratios of the main reinforcement are as follows. Table 3.8.5 Minimum/maximum steel ratios of the main r min

▶ Without application of seismic design criteria é ù f r min = max ê0.26 ctm , 0.0013ú f yk ëê ûú ▶With application of seismic design criteria r min = 0.5

r max

f ctm f yk

User-specified

2) She ar strength The design shear strength must exceed the required shear strength. The shear reinforcement spacing must be less than the maxim um spacing limit set by industry standards. V Ed £ V Rd

(3.8.12)

s £ s max

(3.8.13)

If concre te takes on the full shear force, steel shear strength may be ne glected. How ever, if the shear force exceeds the resisting force of the concrete, then the shear steel will take on the full shear load. Using these assumptions, the design shear strength can be calculated as follows:

ìV Rd ,c (V Ed £ V Rd ,c ) V Rd = í îV Rd , s (V Ed > V Rd ,c )

(3.8.14)

The shear force taken on by the concrete is calculated as shown below. Typically, designs consider σ cp , but this program do es not consider axial forces. Thus, σc p =0 and the shear forces are calculated accordingly.

V Rd ,c1 = C Rd ,c k (100 r l f ck ) bd 1/ 3

(3.8.15)


DESIGN REFERENCE


V Rd ,c 2 = vminbd V Rd ,c = min[V Rd ,c1 , V Rd ,c2 ]


(3.8.16) (3.8.17)


DESIGN REFERENCE

Here,

C Rd ,c =

0.18

g c

é

200

ë

d

k = minê1 +

ù

, 2.0ú

û

é A ù r l = minê sl , 0.02ú ë bd û k 1 = 0.15 1/ 2 vmin = 0.035k 3 / 2 f ck

Shear force taken on by the shear reinforcement steel is com puted as shown below .

V Rd , s1 =

A sw s

zf wd cotq V Rd ,max =

(3.8.18) a cwbzv1 f cd

cotq + tanq

(3.8.19) V Rd , s = min[V Rd , s1 , V Rd ,max ]

(3.8.20)

Here, z = 0.9d a cw = Factor that incorporates the compressive stress state. In beams, axial force is neglected and thus

σ cp =0, meaning a cw =1.0.

Table 3.8.6 Recommen de d

Criteria

αcw

values of α c w fo r non-

0< σ c p ≤ 0.25f cd

1+ σ cp / f c d

prestressed structural

0.25 f cd <σ cp ≤ 0.5f cd

1.25

0.5 f cd < σ cp ≤ 1.0f cd

2.5(1-σ cp / f cd )

q = Angle of the compressive concrete struts. Applies user-specified values


DESIGN REFERENCE


Maximum spacing limits for the shear reinforcement is a function of the seismic de sign criteria and the calculations are shown below.

Table 3.8.7 Maximum spacing limits for s hear reinforcement, as a function of seismic design criteria

Without applying seismic design criteria

This program only considers vertical shear reinforcements, and thus, by assuming a = 90° , sl ,max = 0.75d (1 + cota ) = 0.75d

▶ Ends (DCM) sl ,max = min[ 0.25 H , 24 D shear , 8Dmain, 225mm] Applying seismic design criteria

▶ E n d s ( D C H) sl ,max = min[0.25 H , 24 D shear , 6Dmain,175mm] ▶ Interior sl ,max = 0.75d (1 + cota ) = 0.75d

Whe n applying seismic design criteria, shear reinforcement shou ld be more den sely arranged in some portions of certain structural membe rs. The length of the m embe r in which a more dense a rrangement is required is calculated as follows: ì1.5 hw (DCH ) l cr = í î1.0 hw (DCM )

(3.8.21)

Minimum steel ratio for shear reinforcement is shown below.

r w,min = 0.08

f ck f yk

(3.8.22)

SLS : Serviceability Limit State The serviceability limit state of beams is checked with respect to stress limits, crack controls, and deflection controls.



DESIGN REFERENCE

1) Stress limits

Concrete com pressive stresses are limited to ensure that longitudinal cracking or other m iscellaneous cracking does not occur. The characteristic load combination (one of the serviceability load combinations) are used to check the stress limits.

s c £ k 1 f ck

(3.8.23)

Moreove r, among the serviceability load combinations, the “Quasi-permanent” load combination is used to compa re its concrete stress and the following limits to determine the linearity of creep.

Table 3.8.8 Criteria for determining creep linearity

s c £ k 2 f ck

Linear creep

s c > k 2 f ck

Nonlinear creep

The tensile stress in the steel is limited to ensure that inelastic strain and excessive cracks/strain do not occur, and is limited using the following equation:

s s £ k 3 f yk

(3.8.24)

The required coefficients for stress checks, k 1 , k 2 , k 3 , k 4 , may be set by the user, and the default values are the recommend ed values in the design code.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.8.4 Dialog window showing set up of Serviceability Limit State

2) Crack control


DESIGN REFERENCE


Cracks ne gatively impact the structure’s performance , and m ust be limited to ensure that appea rance is not excessively altered, using the following inequality:

w k £ w max

(3.8.25)

Creep wid th w k is calculated as show n below.

(3.8.26)

wk = sr ,max (e sm - e cm ) Figure 3.8.5 Creep width w k , at the same distance from the concrete edge as the rebar spacing

Here, s r ,max = k 3c +

f

k 1k 2 k 4f r p ,eff

(3.8.27)

= Steel diameter. If various steel diameters are used, the equivalent diameter f eq is computed

and used instead. f eq =

n1f 12 + n2f 22 n1f 1 + n2f 2

c = Longitudinal steel cover distance. k 1

= Factor that incorporates steel’s bond ing characteristics. This program uses a value of 0.8.



DESIGN REFERENCE

k 2

= Factor that incorporates strain distribution. This program u ses a value of 0.5.

k 3 = 3 . 4

k 4 = 0.425

s s - k t e sm - e cm =

f ct ,eff r p ,eff

(1 + a r e

p , eff

E s

s s

= Tensile stress of the steel, assuming cracked section.

k t

= Factor depending on the load period.

) ³ 0. 6

s s

(3.8.28)

E s

- Short term loading : 0.6 - Long term loading : 0.4 f ct ,eff = f ctm a e =

E s E cm

r p ,eff =

=

E s

æ f ö 22ç cm ÷ è 10 ø

A s + x 12 Ap ' Ac , eff

=

0.3

As Ac ,eff

Ac,eff = bhc,ef

é ë

hc,ef = minê2.5( h - d ),

h - x 3

,

hù 2 úû

Figure 3.8.6 Effective tension area (typical cases)


DESIGN REFERENCE


The crack width limit w ma x is decided based on the exposure category and applied load combination, and the limits are provided by the design code as shown below. This program distinguishes between the quasi-permanent and frequent load combinations, and uses the user-specified w ma x .



DESIGN REFERENCE

Table 3.8.9 Crack width limit w m a x for various exposure categories and ap plied load

Exposure category

X0 XC1

Serviceability Load Combination Type Quasi

Frequent

Characteristic

0.4

XC2 XC3

0.3

XC4

Not

XD1 XD2

Checked

0.3

XD3 XS1 XS2

0.3

User-Specified

XS3 XF1* XF2* XF3* XF4* XA1*

Not Checked

0.2 (Incorporates randomness)

XA2* XA3*

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.8.7 Dialog window for setting crack width limits

3) Deflection Che cks


DESIGN REFERENCE


Excessive deflection negatively impacts the structure’s performance and appearance, and can also damag e nonstructural components. The actual deflection deflection must be less than the allowable deflection: deflection:

d actual £ d allow

(3.8.29)

The actual deflection is the product of the analyzed deflection and load combination factors. The allowable deflection deflection ap plies the user-specified user-specified design mem ber length.

Home>D esign Settings Settings>General >General>Design >Design Code>RC >Code-Specifi >Code-Specificc RC Design Parameters Figuree 3.8. Figur 3.8.88 Dialo Dialogg window for setting deflection controls

154 | Sec Section tion 8. Mem Membe berr Examinat Examination ion Proce Procedure dure (Beams) - EN1992-1-1:2004


DESIGN REFERENCE

Se ction ction 9

Member

Examination

Procedure (Columns/Braces) -EN1992-1-1:2004 The memb er verificati verification on procedure for for RC columns/braces following following the the EN1992-1-1:2004 design code is explained in this section. The design strength is calculated using the analyzed strengths, load combinations, and design strength modification modification factors. factors. Design code strengths are computed to verify the axial strength strength and flexural strength.

Section Sect ion 9. Member Examina Examination tion Procedure Procedure (Columns/Braces) - EN 1992-1-1:2004 | 15 155 5

DESIGN REFERENCE

156 | Sec Section tion 9. Mem Membe berr Examina Examinatio tion n Procedu Procedure re(Column/Braces) - EN 1992-1-1:2004



DESIGN REFERENCE

Calculating Calculating de sign forces/dema forces/dema nds The d esign forces are calculated, calculated, factoring factoring in the live load reduction factors, mome nt ma gnifiers, gnifiers, and special seismic design criteria

1) App licati lication on of load comb inations inations

2) Application of live load reduction factors As explained in the section Design Fa ctors>Live Load Reduction Fa ctors, ctors, compo nents that are subject to live loads will have design forces that incorporate the live load reduction factor.

3) App licati lication on of m omen t magn ifiers ifiers When designing columns and braces, if the slenderness ratio exceeds the slenderness limit, then second order effects must be accoun ted for and the design mome nt is calculated calculated as follows.

M Ed = M 0 Ed + M 2

(3.9.1)

Here, M 0e = max[0.6 M 02 + 0.4 M 01 , 0.4 M 02 ] ( M 02 ³ M 01 )

M 2 = N Ed e2 = N Ed 1 r

1

= K r K f

r 0

1 l 02 r c

= K r K f

e yd 0.45d

é nu - n ù ,1.0 ú ë nu - nbal û

K r = max ê n u = 1 + w

w =

n=

A s f yd Ac f cd

N Ed Ac f cd

Section Sect ion 9. Member Examina Examination tion Procedure Procedure (Columns/Braces) - EN 1992-1-1:2004 | 15 157 7

DESIGN REFERENCE


n bal = 0 .4

Kφ = a factor that incorporates creep effects, This program do es not consider creep, so the value is set to be 1.0.

158 | Section 9. Member Examination Procedure(Column/Braces) - EN 1992-1-1:2004


DESIGN REFERENCE

4) Application of special seismic design criteria Whe n seismic design criteria are being applied, design shear is calculated using the strong shearweak b ending principle and the load com bination that includes ea rthquake loads, as shown below.

Table 3.9.1 Shear force calculations for seismic design purposes, using the strong shear-weak bending principle

V e1,cw,1 = V g +

M i,d ,i ( + ) + M i ,d , j ( - )

V e1,cw, 2 = V g -

[

V e1,ccw,1 = V g +

l n M i ,d ,i ( + ) + M i ,d , j ( - )

V e1,ccw, 2 = V g -

l n


M i ,d ,i ( - ) + M i,d , j ( + ) l n M i ,d ,i ( -) + M i ,d , j ( + ) l n

[

]


]


The en d mo ments, Mi,d, required for calculating design shear forces, is computed as follows: é

M i,d = g Rd M Rb,i min ê1,

êë

å M å M

ù ú Rb ú û Rc

(3.9.2)

Here, γ Rd

= F actor that incorporates the increased strength due to steel strain hardening Specified by the user in Design S etting

M Rb,i

= Design end moment.

ΣM R c

= Sum o f the design mome nts at the column nodes

ΣM R b

= Sum o f the design mome nts at the beam nod es.

Home>D esign Settings>General>Design Code>RC >Code-specific RC D esign Parameters Figure 3.9.1 Dialog window showing the setup of γ R d for desi n shear force

Section 9. Member Examination Procedure (Columns/Braces) - EN 1992-1-1:2004 | 159

DESIGN REFERENCE




DESIGN REFERENCE

ULS: U ltimate L imit State 1) Axial-lateral strength

The design strengths of members subject to both axial and lateral loading must incorporate the P-M correlation. In this program, the P-M correlations are incorporated into the computation of axial and lateral strengths. The main reinforcement ratio must satisfy the minimum and m aximum s teel ratio limits. N Ed £ N Rd

(3.9.3)

M Ed £ M Rd

(3.9.4)

M Edy £ M Rdy

(3.9.5)

M Edz £ M Rdz

(3.9.6)

r min £ r £ r max

(3.9.7)

Column/brace memb ers sub ject to bo th axial and lateral loads must satisfy force equilibrium and strain compatibility criteria. Stress-strain relationships for biaxial P-M correlations are shown below. Figure 3.9.2 Stress strain relationships for Biaxial P-M correlation curves


DESIGN REFERENCE


The ax ial force and lateral moment is calculated using eccentricity. Using the resulting values, the P-M correlation curve is calculated. Throug h the correlatio n cu rve, the design strength co rresponding to the desired force may be found.

Figure 3.9.3 Biaxial PMcorrelation


DESIGN REFERENCE


Figure 3.9.4 P-M correlation for a specific load combination


DESIGN REFERENCE


The minimum and ma ximum steel ratios for the main reinforcement are shown be low.

Table 3.9.2 Minimum and maximu m steel ratios for the main reinforcement

é 0.10 N Ed

r min

maxê

r max

User-specified

êë f yd Ac

ù

, 0.002ú

úû

2) Shear strength

The design shear strength must be greater than the expected design shear demands. The main reinforcemen t spacing must be sma ller than the maximum spacing limits set by the design code.

V Ed £ V Rd

(3.9.8)

s £ sl ,max

(3.9.9)

If concrete takes on the full shear force, steel shear strength ma y be neglected. However, if the shear force exceeds the resisting force of the concrete, then the shear steel will take on the full shear load. Using these assum ptions, the design shear strength can be ca lculated as follows:

ìV Rd ,c (V Ed £ V Rd ,c ) V Rd = í îV Rd , s (V Ed > V Rd ,c )

(3.9.10)

The shear force taken on by the concrete is shown below.

[

V Rd ,c1 = C Rd ,c k (100 r l f ck )

1/ 3

+ k 1s cp ]bd

(3.9.11)

V Rd ,c 2 = (vmin + k 1s cp )bd

(3.9.12)

V Rd ,c = min[V Rd ,c1 , V Rd ,c2 ]

(3.9.13)

Here,



DESIGN REFERENCE

C Rd ,c =

0.18

g c

é

k = minê1 +

ë

ù 200 , 2.0ú d û

é A ù r l = minê sl , 0.02ú ë bd û k 1 = 0.15 1/ 2 vmin = 0.035k 3 / 2 f ck

The sh ear strength taken on by the shear reinforcemen t is calculated as follows:

V Rd , s1 =

A sw s

V Rd ,max =

zf wd cotq

(3.9.14)

a cwbzv1 f cd

(3.9.15)

cotq + tanq

V Rd , s = min[V Rd , s1 , V Rd ,max ]

(3.9.16)

Here, z = 0.9d a cw

Table 3.9.3 Factor that incorporates the compressive stress state, α cw

v1

= Factor that incorporates the compressive stress state Criteria

α cw

0< σ c p ≤ 0.25f cd

1+ σ cp / f c d

0.25 f cd <σ cp ≤ 0.5f cd

1.25

0.5 f cd < σ cp ≤ 1.0f cd

2.5(1-σ cp / f cd )

= S trength reduction factor due to cracked concrete section

Table 3.9.4 Strength

f yw d < 0.8f yw k f yw d ≥ 0.8f yw k

reduction factor due to cracked concrete section

f ck ≤ 60MPa

v1

é ë

v1 = v = 0.6ê1 -

f ck ù

250 úû

v1 = 0. 6

f ck > 6 0M Pa é ë

v1 = maxê0.9 -

f ck

ù û

, 0.5ú 200

q = Angle of the compressive concrete struts. Applies user-specifie d values Section 9. Member Examination Procedure (Columns/Braces) - EN 1992-1-1:2004 | 165

DESIGN REFERENCE


The m aximum spacing limits for shear reinforcement is calculated based on the seismic design criteria, as shown below. Table 3.9.5 Shear reinforcement maximum spacing limits as a function of the seismic d esign criteria

Without applying seismic design

sl ,max = min[ 20d L , B, H , 400 mm]

criteria ▶

Applying seismic design criteria (Ends)

D CM

é b0 ù ,175 mm, 8d bL ú ë2 û

sl ,max = minê

▶ D CH é b0 ù ,125 mm, 6d bL ú ë3 û

sl ,max = minê

Applying seismic design criteria

sl ,max = min[ 20d bL , B, H , 400 mm]

(Interior)

Whe n applying seismic design criteria, there are portions of the m ember in w hich shear reinforcement may need to be more densely arranged. The length of this section of the member is calculated as shown below. l cl ì é ù ïï max ê1.5hc , 6 , 600 mm ú ( DCH ) ë û l cr = í l é ù ïmax 1.0hc , cl , 450 mm ( DCM ) êë úû ïî 6

(3.9.17)

The m inimum steel ratio for shear reinforcemen t is calculated as follows:

r w,min = 0.08


f ck f yk

(3.9.18)


DESIGN REFERENCE

SLS : Serviceability Limit State The serviceability limit state of columns is checked with regards to stress and deflection limits.

1) Stress limits Concrete com pressive stresses are limited to ensure that longitudinal cracking or other m iscellaneous cracking does not occur. The characteristic load combination (one of the serviceability load combinations) are used to check the stress limits.

s c £ k 1 f ck

(3.9.19)

Moreover, among the serviceability load combinations, the “Quasi-permanent” load combination is used to compa re its concrete stress and the following limits to determine the linearity of creep. Table 3.9.6 Criteria for determing cree p linearity

s c £ k 2 f ck

Linear creep

s c > k 2 f ck

Nonlinear creep

The tensile stress in the steel is limited to ensure that excessive cracks/strains do not form, and is limited using the following equation:

s s £ k 3 f yk

(3.9.20)

The required coefficients for stress checks, k 1 , k 2 , k 3 , k 4 , may be sp ecified b y the user, and the d efault values are the recommend ed values in the design code.


DESIGN REFERENCE


Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.9.5 Serviceability limit state settings window

2) Deflection checks Excessive deflection negatively impacts the structure’s performance and appearance, and can also damag e nonstructural compone nts. The actual deflection must be less than the allowable deflection:

d actual £ d allow

(3.9.21)

The actual deflection is the product of the analyzed deflection and load combination factors. The allowable deflection ap plies the user-specified design mem ber length.

Home>D esign Settings>General>Design Code>RC >Code-Specific RC Design Parameters Figure 3.9.6 Dialog window for setting deflection controls



DESIGN REFERENCE

S e c t io n 1 0

Rebar/Arrangement In this program, the user-specified reinforcement information is used as the basis for RC me mbers an d suggests steel rebar arrange ments that satisfy strength and steel detail requirements.

Rebar/Arrangeme nt Settings Conditions for setting rebar/arrangement information for RC members can be set in Home>Design Setting or Design Calculation Option>Reba r Arrangement .

Home>Design Setting>Rebar/Arrangement Figure 3.10.1 Design Setting dialog window


DESIGN REFERENCE


Run D esign>Design Calculation Option

Figure 3.10.2 Rebar Arrangem ent dialog window

When pressing the rebar arrangement button, the following dialog window will pop up in which rebar settings for various membe r types can be set. Figure 3.10.3 Dialog window for rebar arrangem ent setting f or v a rio u s m e m be r t e s

▶ Beam s: Rebar information is specified depending on the section height. Table 3.10.1 Rebar information for beam

Main reinforcement

members Shear reinforcement

Outer reinforcement


Minimum /maxim um diame ters and maxim um num ber of rebars are specified. A list of diameters ranging from the minimum to maximum diameter is created and the most efficient rebar/arrangement is com puted. Minimum/maximum diameters, minimum/maximum spacing, and spacing increment are specified. A list of combinations of the diameters, spacing, and spacing increments are created and the most efficient rebar/arrangement is computed. Minimum/maximum diameters are defined. A list of diameters ranging from the minimum to maximum diameter is created and the most efficient rebar/arrangement is computed.


DESIGN REFERENCE

▶ Columns/Brace s: Rebar information is specified depending on the minimum section measureme nts. Table 3.10.2 Rebar information for c olumn/brace members

Main reinforcement

Minimum/ma ximum d iameters are specified. A list of diameters ranging from the minimum to maximum diameter is created and the most efficient rebar/arrangement is computed. Minimum/maximum diameters, minimum/maximum spacing, and spacing

Shear reinforcement

increment are specified. A list of combinations of the diameters, spacing, and spacing increments are created and the most efficient rebar/arrangement is comp uted.

▶ Plate: Rebar information is specified depending on the minimum thickness. Table 3.10.3 Rebar

Minimum/maximum diameters, top reinforcement units, lower reinforcement

information for plate mem bers

Main reinforcement

Shear reinforcement

units, minimum /maximum sp acing, and spacing increments are specified A list of combinations of the diameters and spacing is created and the most efficient rebar/arrangem ent is com puted.

Minimum/maximum diameters, minimum/maximum spacing, and spacing increments are specified. A list of combinations of the diameters and spacing is created and the most efficient rebar/arrangement is comp uted.

RC Beam Main Reinforcement Rebar/Arrangement The be am’s main reinforcement rebar/arrangem ent compu tation process is as follows.


DESIGN REFERENCE


The requ ired steel amou nt for main reinforcement is calculated by assum ing a singly reinforced beam and computing the design strength equation accordingly. This equation is used to compute the required steel amounts, and in the case of AC I318-11, the calculations are as follows: C = 0 . 85 f ck ab

(3.10.1) T = A s f y

(3.10.2) C = T 에 서 ,

(3.10.3) a=

A s f y 0.85 f ck b

(3.10.4) æ è

M u £ f M n = f A s f y ç d -

f

1

f y2

2 0 .85 f ck b

(3.10.6)


æ 1 A s f y ö ÷ , Rearranged with respect to A s ÷ = f A s f y çç d 2 ø 2 0.85 f ck b ø÷ è a ö

A s2 - f f y dA s + M u = 0

(3.10.5)


DESIGN REFERENCE

The required steel amount calculated following the above procedure and the user-specified main reinforcemen t diameter list are used in conjunction with the design code rebar requirements to create the mo st efficient main reinforcement rebar a rrangement. The main reinforcement diameter list begins from the smallest diameter and finds the rebar arrangemen t that works best for the given section. The num ber of rebars in a single layer is calculated based on the rebar arrangement information, required steel ratio, and the spa cing limitations. As pe r ACI318-11, the following items are considered.

Table 3.10.4 Number of rebars arranged for a single layer, as per ACI318-11

Numb er of required bars based on the steel clear cove

4 é ù dist clear = maxêd b , 1 in, d gravel ú 3 ë û

é

ù ú ë (Splice Ratio )d b + dist clear û

(Maximum number of rebars)

nrebar = FLOOR ê

Num ber of bars based on the

s a = min ê15

tensile steel spacing limiations

é

40000

ë

f s

b - 2 d c + dist clear + d b

- 2.5cc , 12

40000 ù f s

ú û

é b - 2d c ù +1 ú ë s a û

(Crack limitations)

nrebar = CEIL ê

Num ber of required rebars

nrebar = CEIL ê

é A s , req ù ú ë A s1 û

The rebar num bers and the steel diameter computed from the above procedure goe s through strength and steel ratio checks. If the numbers do not pass these checks, then the rebar arrangement for the next diameter is computed and checked.


DESIGN REFERENCE


RC Co lumn Rebar Arrangement Main reinforcement rebar arrangement for column m embe rs is as follows.

Columns are subject to P-M correlation relationships and thus all load combinations must be considered to obtain the m ost accurate results. However, for the efficiency of rebar com putations, the governing load com bination by finding the com bination that yields the greatest required steel amoun t. Additionally, the user-specified m ain reinforcemen t diameter list and rebar design cod e requirements are incorporated in computing the main reinforcement rebar arrangement. The main reinforcement diameter list is searched, starting w ith the sma llest diame ter, until the rebar arrangement that satisfies the load dema nds and the given section is found. 174 | Section 10. Rebar/Arrangement

Midas Ngen Manual

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